National Academies Press: OpenBook

Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop (2016)

Chapter: 3 Computational and Analytical Methods in Additive Manufacturing

« Previous: 2 Theoretical Understanding of Materials Science and Mechanics
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

3

Computational and Analytical Methods in Additive Manufacturing

The second sessions of the first two days of the workshop provided an overview of novel computational and analytical methods for fully characterizing process-structure-property relations in additive manufacturing (AM) processes for materials design, product design, part qualification, and discovery/innovation. This includes multiscale modeling, computational materials, modeling topology optimization, verification and validation methods, and uncertainty quantification for AM processes and AM resulting materials.

Anthony Rollett (Carnegie Mellon University), Wayne King (Lawrence Livermore National Laboratory), Corbett Battaile (Sandia National Laboratories), David Snyder (QuesTek Innovations), Gregory Wagner (Northwestern University), and Joe Bishop (Sandia National Laboratories) each discussed research, challenges, and future directions relating to the following questions:

  • What are computational methods and approaches for simulating materials processing, properties, and performance relationships for materials design using AM as well as key process parameter identification and process mechanics?
  • How can high-performance computing spanning scientific discovery be leveraged with ensembles of engineering solutions?
  • How can topological design loops be integrated with AM processes and mechanics within a computational framework?
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
  • How can AM benefit from fundamental advances in verification, validation, and uncertainty quantification methodologies?
  • What analytical, experimental, and software tools are needed?
  • How can new tools be integrated to impact adoption of AM?
  • What opportunities exist for high-performance computing in order to provide fundamental scientific discovery of the process-properties-performance relationship relevant to AM?
  • What are the drivers and the fundamental advancements needed for computational methods and optimization techniques?

COMPUTATIONAL AND ANALYTICAL NEEDS IN ADDITIVE MANUFACTURING

Anthony Rollett, Carnegie Mellon University

Anthony Rollett began by adding two additional questions to the session topics that he believes should be considered:

  1. Is there sufficient funding in the United States for fundamental research and development for AM?
  2. Most U.S. academic institutions house their AM programs in mechanical engineering departments, and materials departments remain largely disengaged. How can we better involve materials science and engineering students and faculty in AM?

He then showed a video of direct metal AM to illustrate the geometric complexity, the relationship between the melt pool and the previous layers, and other complicated dynamics at play in AM. Carnegie Mellon University (CMU) has a NextManufacturing Center with equipment for AM with metals and polymers, as well as metrology. CMU encourages industrial partners to use this equipment on a fee basis while also providing training on AM equipment.

The state of the art for direct metal AM is advancing, according to Rollett. While there are some estimates indicating that AM parts are not cost-effective versus traditionally manufactured parts, he noted that these often ignore the time savings that AM can provide. Most three-dimensional shapes can now be additively produced directly out of metals with nearly 100 percent density and features down to 200 microns. Parts with volumes

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

up to 10 in × 10 in × 8 in can take from a few hours to over a day each to build. AM parts are currently being used commercially, including a GE fuel nozzle and other parts going into commercial jet engines. The current processes were developed to allow shapes to be built but there can be significant residual stress in as-built parts. Certification and qualification are non-trivial considerations since the materials can vary in their microstructure and defect structure compared to conventionally manufactured parts. CMU is mapping all direct metal processes across their alloy systems, Rollett explained, noting their results can differ due to varying thermal properties.

He commented that almost all metal manufacturers are considering direct metal AM. A crucial step to identifying components as good or bad for AM is to map part specification to AM technical capabilities. While AM benefits are most notable when parts are redesigned specifically for AM, it typically takes users 6 to 12 months to become proficient in AM techniques. He commented that understanding simple trends in processing behavior can have a notable impact. Rollett illustrated this point using a beam power versus beam travel speed map for an electron beam process to infer process behavior. In particular, build rate scales with power, process precision scales with melt pool size, and the beam can stay on straight lines while increasing power to maintain precision and increase build rate. He emphasized that a road map such as this does not give a user all the necessary information, but adding information can help fill in some of the gaps.

There are several challenges when working with AM powders, Rollett explained. First, specific AM approaches require small powder particles but the majority of powder produced is larger than the machines can use. He commented that the community needs a better understanding of fluid flow to optimize production of small powder. Cost is also a concern as Ti-6Al-4V powders for machines cost approximately $250-650/kg and commonly contain voids that can lead to porosity in parts. There is little room for competition because powders have to be purchased from the manufacturers to uphold equipment warranties. An approach to reducing costs, he stated, would be to explore the use of larger size powders in an application that allows rougher surface.

Powder characteristics are related to flow behavior, and Rollett stated it is important to realize that powder particles are often irregularly shaped with satellites attached and other abnormalities and can have unexpected size distributions. These size differences are not necessarily detrimental to AM and can actually improve the process in some situations. He noted that the modeling community could assist in improving control of powder production.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

Pores (including voids in particles, keyhole defects, and incomplete fusion) are common in most materials, even those not typically associated with porosity (e.g., stainless steel), and can affect long-term fatigue performance (Magnusen et al., 1997). Prediction of porosity is a complex problem because the geometry of melt pools is complex; the pools overlap across layers, and there can be regions of unmelted material resulting in lack of fusion porosity. However, models are being developed that appear to match well with experimental data (Ming, Pistorius, and Beuth, 2015).

Rollett raised two issues of importance for AM: variability and fatigue measurements. Variability can come from a variety of sources, including local part geometry and melt pool size and shape, and can have significant ramifications for part reliability and reproducibility. He mentioned the importance of comparing fatigue resistance and strength of AM parts with those produced by traditional manufacturing (Juvinall and Marshek, 2006).

Rollett reiterated that the microstructures of AM parts can vary from those of traditionally manufactured parts. In particular, the melting and cooling process and post-build heat treatments can transform the microstructure, and it is important for users to realize that materials with these different microstructures will respond differently.

Lastly, Rollett emphasized that advanced AM experimental capabilities often require supercomputer resources for data reduction, reconstruction, and analysis. He stressed that these challenges cannot be underestimated. However, analyses of smaller data sets can pose their own challenges as well. In conclusion, Rollett offered the following suggestions in response to the overarching session questions:

  • Heat, fluid, and particle flow; stress-strain including crystal plasticity; and computational thermodynamics are key computational methods and approaches for simulating AM materials processing, properties, and performance relationships.
  • High-performance computing can be utilized to enhance AM-specific capabilities and validate codes against experiments.
  • Computational approaches to understanding AM processes and mechanics may require a multiscale approach.
  • AM can benefit from improvements in real-time data access via data analytics and state-of-the-art characterization.
  • High-performance computing offers the potential for both analysis of large-scale experiments (e.g., synchrotron X-rays) and large-scale simulations with ever-increasing resolution.
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
  • There is likely insufficient U.S. funding for fundamental research and development for AM.
  • Research funding as well as internships and scholarships directed at AM could help engage materials science and engineering students and faculty in AM.

He highlighted the following objectives as being important to the AM community:

  • Integrating, scaling up, and homogenizing detailed modeling of heat, fluid, and energy flows into reduced-order models;
  • Setting up data sharing that is useful for data analytics but also fair to the groups that contribute the data;
  • Supporting industry with basic research that impacts practical issues (e.g., powder manufacture, qualification);
  • Incorporating materials microstructure (e.g., orientation, lattice strain) into continuum codes; and
  • Utilizing big data techniques to deepen the validation process (e.g., use reconstructed images or diffraction data).

HIGH-PERFORMANCE COMPUTING AND ADDITIVE MANUFACTURING: OVERCOMING THE BARRIERS TO MATERIAL QUALIFICATION

Wayne King, Lawrence Livermore National Laboratory

Wayne King began by referencing a recent survey in which 42 percent of companies indicated that poor part quality is a barrier to adopting AM. He stated that modeling and simulation are foundational to qualification, but it is not always obvious how to approach this important part of the process. The work King presented was a collaborative effort1 at LLNL over the last few years.

Modeling of the AM process began in 1998 and included metal thermal modeling (Contuzzi, Campanelli, and Ludovico, 2011; Dai, Li, and Shaw, 2004; Kolossov et al., 2004; Roberts et al., 2009), metal thermo mechanical models (Hussein et al., 2013; Matsumoto et al., 2002), polymer powder-bed fusion (Williams and Deckard, 1998), residual stress modeling (Zaeh

___________________

1 Collaborators include Wayne King, Andy Anderson, Robert Ferencz, Neil Hodge, Chandrika Kamath, Saad Khairallah, Ibo Matthews, and Sasha Rubenchik.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

and Branner, 2010), and laser-powder interaction (Fischer et al., 2003; Gusarov and Smurov, 2010; Tolochko et al., 2003). King commented that much of this work has been concentrated outside the United States.

Modeling metal AM processes is challenging because a broad range of length and time scales are covered. King explained that LLNL researchers use multiscale modeling approaches to provide key insights into AM metal processes that will inform performance simulations. The goal is to link powder, microstructure, and process-aware models through information-passing to inform a performance model and an effective medium model, as shown in Figure 3-1. The powder model and the effective medium model (on the scale of the part) were the focus of this presentation.

The effective medium model that King and his collaborators developed utilizes LLNL’s high-performance computing Diablo code (Hodge, Ferencz, and Solberg, 2014). Diablo facilitates prediction of material behaviors on the scale of the part and is suitable for complex structural response and temperature-driven deformations. He showed an example of a simulation of building a cubic centimeter cantilever part to design a residual stress sample. He commented that there are a number of alternative approaches to doing part-level thermo mechanical models, including custom codes (Denlinger and Michaleris, 2015; Pal et al., 2014; Neugebauer et al., 2014a; Neugebauer et al., 2014b) and commercial codes (Schilp et al., 2014; Seidel et al., 2014; Krol, Branner, and Zaeh, 2009).

The powder-scale model developed by King and his collaborators uses the ALE3D code to perform a first full-physics simulation of laser powder-bed fusion. The physics incorporated include melting and solidification, solidification shrinking, phase transformations and separation, multistructural evolution, convection, heat conduction, radiation, absorption, vaporization, capillary forces, Marangoni convection, gravity, powder layer, and wetting and dewetting. He explained that first principles calculations are being used to understand the absorptivity of the metal powder. The powder size (typically tens of microns) is much larger than the laser wavelength (1 μm), so ray tracing can be used. The refractive index of the metals involved is known or can be measured. On each reflection, the absorption is determined by Fresnel formulas, which include angular and polarization effects. Multiple scattering plays an important role.

Using the commercial code FRED2 for ray tracing with considerable

___________________

2 The website for FRED software is http://photonengr.com/software/, accessed August 16, 2016.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Image
FIGURE 3-1 Multiscale modeling approaches for metal additive manufacturing. SOURCE: Wayne King, Lawrence Livermore National Laboratory, presentation to the workshop.
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

post-processing, King explained that approximately half of the energy is absorbed by the top layer of powder particles, nearly half of the energy is reflected, and only a small portion of the energy leaks through to the underlying layer. Recoil pressure, he explained, occurs when the laser hits a powder particle and the particle quickly reaches the boiling point. The particle rapidly starts evaporating and the evaporating metal jet exerts a force on the liquid, pushing it out of the laser path, therefore allowing the laser to reach the substrate. Using mesoscopic three-dimensional simulations that integrate recoil pressure, King and his collaborators showed that thermal conductivity is a small contributor to the melting process compared with the effects of the recoil pressure.

There are alternative approaches to simulating this as well, King noted, including two-dimensional Lattice Boltzmann methods (Klassen, Scharowsky, and Körner, 2014; Körner, Attar, and Heinl, 2011; Körner, Bauereiß, and Attar, 2013), three-dimensional open-source models (Gurtler et al., 2013), and three-dimensional discrete element methods (Ganeriwala and Zohdi, 2014).

Simulation uncertainty quantification and experimental comparisons are an essential component to AM modeling, King stressed. Experiments can reveal missing physics in simulations. He showed an experimental video similar to the setup of the ALE3D powder simulation. Experiments show the melt pool expansion exerts a forward push on powder and the nearby powder is consumed through capillary forces into the melt pool, similar to the simulation. However, non-local powder experiences inward force toward the melt pool, unconsumed cold powder is swept backward and upward, and molten droplets eject in both directions directly from the melt pool. Experiments also observed a forward ejection at high scan speed and high power and a faint vapor trail at higher power.

He also discussed options for improving efficient predictions, including combining advanced sampling with a Gaussian process code surrogate. This has the potential to more quickly highlight regions of power and speed space that could be viable, therefore making further studies more effective. In conclusion, King summarized the issues and challenges in powder and part-scale models. The powder model needs the following:

  • A better laser absorption model,
  • An approximation of some physics,
  • Thermophysical properties over a broad range of temperatures,
  • Fine zoning,
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
  • Explicit time marching to limit time step,
  • Experimental data, and
  • Inclusion of evaporation and flowing cover gas effects.

The part-scale model has the following challenges:

  • Disparate spatial scales of the laser energy source and the overall part geometry,
  • Disparate time scales of local heating versus overall heat transfer and the actual time of fabrication, and
  • Scant handbook-type property data available for high temperatures.

REVOLUTIONS IN DESIGN AND MANUFACTURING: TOPOLOGY OPTIMIZATION AND UNCERTAINTY QUANTIFICATION IN ADDITIVE MANUFACTURING

Corbett Battaile, Sandia National Laboratories

Corbett Battaile began by noting that his presentation would focus on design, specifically his team’s work at Sandia National Laboratories.3 He explained that topology optimization is a way to determine an optimal shape to best achieve a set of desired objectives, performances, or specifications using a distribution of materials and set spatial constraints. Traditional manufacturing sets constraints on how manufacturing is approached, but these constraints are loosened for AM. The design process can therefore take a more prominent role with AM than it has had in traditional manufacturing. He showed an example of a lantern bracket designed via topology optimization, where the material and the spatial constraints were defined and the shape was developed to optimize mechanical characteristics and behavior.

Design for traditional manufacturing has been revolutionized in recent decades, moving from drafting by hand to computer-aided design (CAD). Now, advances in manufacturing are furthering design capabilities, including the establishment of the Plausible Topology Optimization program (PLATO), developed at Sandia National Laboratories. The goal for design of AM parts mirrors AM motivations in general, Battaile explained, including the desire to be affordable, agile, and assured. This new design flexibility

___________________

3 Collaborators include Miguel Aguilo, Ted Blacker, Andre Claudet, Brett Clark, Ryan Rickerson, Josh Robbins, Louis Vaught, and Tom Voth.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

affords many great opportunities, but significant challenges include in situ material qualification and characterization, specifically how to address and integrate the process-structure-properties hierarchy for this new class of materials with complicated microstructures.

The utilization of topology optimization is an inversion of the conventional design paradigm, which in turn leads to an inversion of the qualification process. As an optimizer is designing a part, Battaile explained, it is doing the continuum analysis to qualify the design as it is evolving. In conventional manufacturing, a form is specified, designed, and then verified using finite element analysis, iterating as needed. Using topology optimization, the design domain and function are first specified, topology optimization using finite element analysis determines the form that meets the function, and then an optimized design is established. Performance prioritization can then be done to define a Pareto suite of topologies evaluating the thermal mechanical properties of the proposed topologies.

Advantages of topology optimization for manufacturing include the opportunity for increased complexity, minimal waste, fast design to manufacturing time, and mixed and graded materials. AM is moving toward point-wise material variability and the optimization needs to be able to account for this when developing the design. Battaile commented that in situ metrology to validate designs could also be built into the optimization process, keeping in mind the computational cost constraints.

To illustrate the point about computation time, Battaile discussed an idealized linear static problem with 1.5 million elements, one objective (to maximize stiffness), one loading condition, and built-in uncertainty quantification. This problem would take approximately 2,000 hours (or 12 weeks) to solve with approximately 4,000 processors, he explained. Researchers at Sandia are looking into ways to reduce this run time using physics-based reduced-order modeling to reduce the finite element resolution and smart sampling techniques to streamline the uncertainty quantification, which can reduce the runtime to approximately 5 hours.

Many steps need to come together to make this approach usable for engineers, he emphasized. The function-based design environment is dependent on a variety of inputs and analyses, as shown in Figure 3-2. A number of tools can be used at each of these steps. Battaile summarized that in topology optimization tools, high fidelity in a modern design and analysis environment with smooth connected shapes and fast convergence is key. Interactivity is important, especially with speed and control, to develop robust designs that can be directly printed and interfaced to a CAD system.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Image
FIGURE 3-2 Function-based design environment. SOURCE: Corbett Battaile, Sandia National Laboratories, presentation to the workshop.

DISCUSSION

Following their presentations, Anthony Rollett, Wayne King, and Corbett Battaile participated in a panel discussion moderated by Steve Daniewicz from Mississippi State University. A participant noted that transferring topology optimization design back into CAD tools is often challenging. Battaile agreed that this is essential; he said they use a tool that is part of Sandia’s CUBIT software,4 and they are working on exporting the geometry directly to CAD software.

Another participant asked if the laser sintering modeling King described includes the possible effects of ionization, which would then create an electrical plasma that could have the forces to produce the motion of the particles. King clarified that the current simulation does not include this force and his impression is that to do so would require a finer resolution mesh and time steps. However, he stated that they know that a plasma pool does form and it would be beneficial to simulate this effect. Rollett added that King’s simulation involved a laser powder bed and, in contrast,

___________________

4 The website for the CUBIT toolkit is https://cubit.sandia.gov/public/tutorials.html, accessed August 16, 2016.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

the electron beam powder bed is typically preheated to sinter the particles together, which would likely lead to very different results.

A participant referenced the intensive computation power required for simulations and noted that even the reduced computational time discussed would still be prohibitive for many researchers. He asked what resources are necessary to make these simulations available to the wider community. Battaile emphasized that this is a major challenge but, fortunately, tools for speeding topology optimization are being developed and computing resources for researchers are growing. He said that much of the promise is not just in taking a finite element analysis and doing a topology optimization on it but rather in integrating this capability with process modeling and material physics calculations. An audience member mentioned that reduced-order modeling holds great potential but has not been widely applied to AM yet. King commented that the goal is to build parts computationally in less time than it takes to build parts physically. Rollett noted that advances in this area will likely depend on a multiresolution approach.

A participant asked how the cm3 model King described is connected with the powder-scale model and why the laser in the cm3 model is wider than he would expect. King responded that the models are linked by information-passing between them. The laser appears large because that is the mechanism by which the models homogenized information-passing. They simulated thick layers with a large laser beam in order to simulate the cm-scale part in a reasonable amount of time.

An online participant asked how access is granted to operators of commercially available machines to obtain and control process parameters (e.g., laser path, beam power and travel speeds). Assuming an AM process can be optimized virtually using numerical simulation, the participant asked if optimized process parameters such as the new laser path or laser power could be readily deployed into the machines. Rollett commented that it would be useful if these parameter values were easier to obtain. Manufacturers protect some information for proprietary reasons, but some open-source machines are being developed. He believes there is hope for optimizing the AM process by treating it as a black box response function since the inputs and outputs are known.

Another participant posed a question to the panel about whether the ray tracing approach is materials-specific and can thus be incorporated in a mathematical model. King stated that while only the complex index of refraction of the material is needed to do the ray tracing approach, this is unknown for many materials. Also, ray tracing works well for some systems

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

(e.g., titanium and stainless steel) but not others (e.g., aluminum). As the laser beam moves, the powder is quickly converted to liquid so the absorptivity of the liquid is the key parameter, not the absorptivity of the powder. For the part-scale model, a volumetric heat source is being considered. A participant asked if the ray tracing approach can be translated to particle size modeling using ALE3D. King said this is already being implemented into the model through a ray-tracing package.

A participant asked how important uncertainty quantification is and if it is related to the final quality of the product or part and in situ monitoring (e.g., data mining, reduced-order modeling). Rollett noted that parts are already being produced successfully with AM and reduced-order modeling is working well, and he questioned whether more detailed modeling is needed. He explained that there is a clear trade-off between tweaking process parameters and the ultimate quality of the part, but there are not clear limits about what could be done. Improving parts can be approached from the top, by bounding variability, or from the bottom, by providing the tools that make the analysis more quantitative. He also mentioned that data mining and data analytics techniques are crucial for understanding the microstructure and other parameters and should continue to be examined.

A participant commented that the computational time of topology optimization is continuing to decrease with advanced computational techniques and resources and that near real-time optimization is possible in the immediate future. Battaile agreed that this is true in a general sense but the metrics can still be intimidating. He clarified that the simulations he discussed are conducting on-the-fly conformal surface meshing in an integrated multiphysics code, which can be computationally costly. There are much more cost-efficient computational approaches to conducting topology optimization, but they may not incorporate the same features and physics.

A participant from a national laboratory asked if the optimization algorithm accounts for either nonlinear geometric constraints (e.g., contact) or processing constraints (e.g., process-dependent residual stresses). Battaile said that he does not believe nonlinear geometric or processing constraints are accounted for at this time. Part of the complicating factor for the geometric constraints is that the topology optimizer starts with a dispersion of material density and then begins to move this around to decide on a shape, so nonlinear constraints are difficult to handle in the mechanical calculations.

The same participant asked if the initial mesh specification could limit the ability of the algorithm to modify the mesh. Battaile said that he is not

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

aware of initial mesh limitations. He and others are currently working to develop adaptive meshing and there have not been any indications of issues. An audience member commented that new generalized finite element and measurement methods may be helpful. Rollett noted there are also image-based techniques that remove the need for a mesh.

Another online participant asked Battaile if the decoupled inverse problems of design, manufacturing, and uncertainty quantification can be combined. For example, could the cost and time consumption of AM and the AM design limitations all be considered in the design process? Or, could the design and manufacturing process be updated on the fly as uncertainties are detected by real-time metrology? Battaile responded that combining design, manufacturing, and uncertainty quantification is an open challenge. Rollett commented that there are a number of related issues from the control perspective that need to be addressed as well. Battaile noted that on-the-fly metrology that connects back with the design process would be a powerful capability.

A question was asked about the connection between simulations and in situ monitoring and measurement. Specifically, the participant noted that experimentalists often view simulations as a way to better understand what was observed experimentally, but the emerging predictive capabilities of models suggest that the community may benefit from adjusting in situ measurement strategies to try to observe phenomena that models are predicting. He wondered if this is a trend in the AM community. King stated that measuring predicted behavior is important but he believes the modeling and simulation could make the most impact in feedback control to enhance the overall quality of AM parts.

A participant commented that hydrodynamics might be important and wondered if King has examined the chemistry of the gas moving backward in his simulation. King agreed hydrodynamics are important and stated there is interplay between the cover gas and the plasma that is being formed. He and his collaborators are hoping to conduct plasma diagnostics to help understand this behavior. The participant asked if the particle size impacts the particles moving toward the melt pool, but King has not examined this area yet. Lastly, the participant asked if the shape of the laser beam impacts defect formation. King stated that a Gaussian laser beam is a poor choice because the boiling temperature will be reached at the center of the beam, and they are examining several other beam profiles.

There was a comment that AM allows for a highly nonuniform material distribution, which works for optimization but is a challenge for structural

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

analysis. Battaile agreed that one of the key issues is understanding when the scale thresholds are crossed and how to deal with scale-specific considerations. He said an open challenge is tying the analysis and physics models across scales to do on-the-fly design.

APPLICATION OF INTEGRATED COMPUTATIONAL MATERIALS ENGINEERING TO THE DESIGN AND DEVELOPMENT OF NEW HIGH-PERFORMANCE MATERIALS FOR ADDITIVE MANUFACTURING

David Snyder, QuesTek Innovations

David Snyder mentioned that computational methods and approaches for materials design and integration would be the focus of his presentation, specifically with respect to computational thermodynamics and mechanistic property modeling. He emphasized the role of materials and process design as well as integrated computational material engineering (ICME)-based qualification for integrating analytical and computational tools.

He began by explaining that QuesTek focuses on applying a computational thermodynamics approach toward alloy and process design, mostly to simulate phase transformations (e.g., solidification and solid-state precipitation and recrystallization) and microstructural constituents (e.g., strengthening phases, impurities, evolution during complex thermal cycling, and post-processing). This type of approach covered multiple length scales, from atomistic density functional theory calculations to macroscale solidification behavior. He explained that the design parameters (e.g., the matrix, strengthening dispersion, grain refining dispersion, austenite dispersion, and grain boundary chemistry) can help link the process variables with the functional requirements.

AM materials respond differently to processing than their conventionally processed counterparts, Snyder noted. There are unique microstructures in both as-built and post-processed conditions, and post-processing responses are driven largely by the complexity of thermal history and the magnitude of residual stresses generated by process. He stated that existing alloys and post-process conditions are not optimized for AM-specific behaviors, resulting in complex microstructures and unreliable AM performance. Snyder highlighted select metallurgical phenomena that need to be considered for different areas of the AM process flow. For raw stock production, he mentioned the impact of exogenous powder contaminants (e.g., oxides)

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

in the stock as a unique AM challenge. For AM processing (e.g., SLM, EB), solidification defects such as hot tearing and incipient melting are a concern, as is quench suppressibility (e.g., cold cracking and transformation stresses). For the post-heat treatment response (e.g., stress relief, HIP), he stressed that additional optimization is needed for recrystallization response (e.g., grain and phase refinement) and precipitation response.

To illustrate these concepts, Snyder provided a couple of case studies from QuesTek. The first was a nickel superalloy study illustrating that residual stresses can drive recrystallization during post-processing. He commented that established materials and processes are not optimized for AM-specific recrystallization response. While there are opportunities to design alloys and processing to tailor behavior for AM, more information is needed to better link models.

The second case study used a titanium alloy (Ti-6Al-4V) to illustrate that proper design of microstructures is critical to predictability and reliability. Current titanium relies on equiaxed, uniform microstructures for strength and ductility. Alloys have been optimized for wrought processing but unique AM microstructures emerge from cooling-rate sensitivity, resulting in substantial variations in a single build. Better understanding the material response is essential but is difficult to model. He emphasized that there are opportunities to use titanium alloys in a way that is more predictable, reliable, and isotropic than what has been observed with Ti-6Al-4V.

The third and final case study he discussed highlighted AM of high-strength aluminum, which is currently limited by hot tearing phenomena where cracks form during the build process. This phenomenon is driven by high residual stress and suboptimal solidification behavior. Currently, aluminum is restricted to low-performance alloys designed for casting since the high-performance alloys designed for forging are not amenable to AM. He stated that there are opportunities to integrate residual stress prediction with solidification theory and design new AM-specific alloys that address crack susceptibility. He elaborated on a project at QuesTek to tailor a new aluminum alloy (Al-Zn-type) to AM needs. Computational optimization between hot tearing susceptibility (processability) and precipitation strengthening (performance) is being used to tailor material behavior.

Snyder highlighted the importance of understanding rare defects associated with exogenous powder contaminants. These inclusions and contaminants are expected to be a confounding factor for fatigue. Many oxides cannot be broken up by the lasers (Thijs et al., 2013; Louvis, Fox, and Sutcliffe, 2011) so process modeling and optimization techniques are

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

needed to mitigate the effects of exogenous defects beyond the impact of porosity, which is being studied.

Snyder also mentioned some computational needs. One issue is that some alloys (e.g., Ti-6Al-4V) are highly sensitive to the AM process; therefore, linkage between process and microstructure is critical. Another issue discussed was select process-microstructure modeling needs, including the linkage between AM process models and solidification theory (e.g., columnar-to-equiaxed transition, cellular-to-dendritic transition, and transformation kinetics), location-specific thermal history (e.g., input into solidification models and phase evolution models), and residual stresses (e.g., input into recrystallization models). He emphasized that better physical understanding of AM processes can drive targeted materials design for more predictable AM components.

Once there are predictable and reliable materials, computational approaches exist to accelerate qualification. The current ICME approach to accelerated qualification of new material and processes couples well-calibrated, mechanistic property models with predictable sources of processing variation to project location-specific properties and design allowables. He suspects these types of coupled approaches will be critical for AM because the AM process is expensive and would benefit from computational experimentation. However, near- and long-term issues exist with applying these approaches to AM. In the near term, process variables that are primary sources of variation are well known in conventional processing but not for AM. Researchers need validated AM process models to provide input into true sources of AM-specific process variation before such methods can see full utilization, he stressed. The AM process is also highly material dependent and is driven by the response to post-processing. A long-term issue is that qualification for AM is really qualification for parts.

Computational advances in AM are crucial for widespread industry adoption, Snyder argued. The physical understanding of how material behaves during AM processing is key to establishing confidence for implementation in industry. Current adoption is restricted by this lack of understanding, and fundamental modeling can shed light on the physics of process to increase industry confidence. He said that modeling can help to down-select key variables for more targeted experimentation. He also argued that coupling in-process monitoring and modeling within an ICME framework is critical for robust production, especially given the significant sources of variability in AM processes. Models that define select quality

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

metrics and are implemented with in-process monitoring to establish confidence intervals would be helpful.

In conclusion, Snyder summarized that predictable materials are needed to enhance build reliability, reduce sensitivity to AM process variables, allow tailored microstructures (e.g., mitigation of AM anisotropy, design for AM-specific defects such as inclusions, and exploitation of AM-specific responses such as rapid solidification and recrystallization), and simplify computational approaches. He suggested that materials design theories are available, but a comprehensive understanding of what makes any material “well-behaved” for AM and how process model insights can facilitate AM materials design is needed.

COMPUTATIONAL AND ANALYTICAL METHODS IN ADDITIVE MANUFACTURING: LINKING PROCESS TO MICROSTRUCTURE

Gregory Wagner, Northwestern University

Gregory Wagner began by discussing linking modeling and simulation of process to performance. He explained that the impacts of process parameters (e.g., laser power, scan speed, scan direction, material, powder size, and layer thickness) and the microstructure (e.g., porosity, grain structure, surface roughness, precipitates, voids, defects, and residual stress) on properties and performance (e.g., strength, fatigue life, ductility, hardness, and toughness) would be the focus of his presentation.

He noted that computational methods and optimization techniques are difficult for AM because of multiple length and time scales, complicated or unknown physics models, and complex moving interfaces. In a typical AM approach for metals (e.g., laser engineering net shapes [LENS], selective laser melting [SLM], or electron beam melting [EBM]), multiple analyses are important, including the following:

  • Powder delivery, using either a feed or bed formation;
  • Heat source, utilizing either a laser or electron beam;
  • Part scale, incorporating heat transfer, phase change, and thermomechanics;
  • Powder and sub-powder scale, including melting and solidification, deformation and flow, and microstructure formation; and
  • Mesoscale, focusing on homogenization to connect the part scale and the powder and sub-powder scale.
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

AM phenomena occur on multiple time and length scales, Wagner commented, which impose serious trade-offs between solution resolution and computational efficiency of simulations. He discussed a method for concurrent multiscale modeling that focuses on the macroscale and simulates the microscale only where needed (e.g., where stress is concentrated or a feature such as an overhang is present). The concurrent approach allows the complicated thermal history and other factors to be imposed on the microscale while also bringing microscale information into the macroscale. This approach can take the form of coupling the part-scale model with what is happening at the melt pool or particle scale.

He gave an example of coupling the macroscale finite element simulations with microscale Thermo-Calc simulations. Thermo-Calc can give properties (such as the enthalpy versus temperature curve) based on composition by solving the local phase evolution or diffusion problem. He showed two simulations comparing a finite element simulation with properties derived through Thermo-Calc, demonstrating the part-scale sensitivity to the microscale.

The goal is to extend this type of coupling to handle the microscale problem by using a multidimensional phase field model to get the solidification structure, he explained. Since large thermal gradients lead to complex microstructure evolution during manufacturing, the local thermal history is used to predict the microstructure. This concurrent multiscale method is approached with fairly simple isotropic phase field models that track the solidification front but will hopefully allow anisotropic microstructure and dendrite formation to be simulated. He emphasized that modeling these phenomena will give greater insight into process control.

Full fine-scale modeling of a part is unrealistic but, according to Wagner, there are opportunities to utilize high-performance computing with reduced-order modeling techniques. This may involve pre-computing large-scale simulation to compute mode shapes for fast approximate solves (Carlberg et al., 2013) or nonlinear dimensionality reduction (or similar methods) to classify and query databases of fine-scale solutions (Tenenbaum, de Silva, and Langford, 2000). To illustrate the complicated and unknown physics models, Wagner gave the example of modeling e-beam heating. He explained that the correct form of the thermal source term due to beam heating is unknown but Monte Carlo simulations of electron-atom interaction may elucidate this (Yan et al., 2015).

In terms of tools for AM, he commented that non-isothermal, multicomponent phase field models for solidification of complex materials are

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

needed. These could be used to examine phase field simulation of martensitic transformation under plastic strain (similar to work done by Kundin, Pogorelov, and Emmerich, 2015). Additional mesoscale models for powder beds with different levels of particle consolidation would also be helpful (e.g., Zhou et al., 2015).

Dealing with model uncertainty is another consideration. Several key parameters in AM are still not well understood, Wagner commented, including how high the temperature gets during AM. He stated the modeling community could do more to help determine what quantities that can be measured will best inform model selection. However, verification of macroscale thermal models is challenging as meshes are refined to the particle scale. Verification needs to be better defined in these cases, he stressed.

Complex moving interfaces are another consideration. He noted that important physics include melting, solidification, flow, vaporization, pore formation, surface tension, conduction, convection, radiation, thermo-capillary motion, and dendrite formation. It would be helpful to be able to combine detailed simulations to capture the evolving interface in a way that is easier to model and run. He commented that progress is being made on modeling powder melt and solidification (King et al., 2015; Markl et al., 2015). Wagner and his collaborators are developing a conservative level set approach to simulate the motion of the liquid vapor interface while simultaneously using a phase field method to track the solid-liquid interface. Conservative level set methods are being used for simulations in multiphase fluid dynamics (Desjardins et al., 2008) and phase field models for fluid-gas interaction (e.g., Kim, 2012; the work of A. Yamanaka at Tokyo University of Agriculture and Technology) have been used to model complex interfaces. Finite cell methods (Schillinger and Ruess, 2015) and extended finite element methods have been used for nonconforming mesh simulations of randomized microstructures (e.g., the work of Jifeng Zhao at Northwestern University). In conclusion, he summarized three main points from his presentation:

  1. Interdependence between scales in AM calls for new computational methods. He noted that concurrent macroscale and microscale simulations should be possible at localized regions of interest and reduced-order models informed by high-performance computing simulations may bring real-time microscale simulations in reach.
  2. Complex physics can be understood through both simulation and experiment. He noted that a coordinated validation plan between modeling and experiments is needed.
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
  1. Methods for modeling complex moving interfaces can impact AM simulations.

ADDITIVE MANUFACTURING CHALLENGES FOR COMPUTATIONAL SOLID MECHANICS

Joe Bishop, Sandia National Laboratories

Joe Bishop stated his presentation would focus on current challenges of computational modeling for solid mechanics, as well as how AM is an interesting application for solid mechanics. He noted that he would be drawing from several projects with many collaborators, including a project on mechanical response of AM stainless steel 304L across a wide range of strain rates,5 and the Predictive Performance Margins Project6 designed to provide a science-based foundation for design and analysis capabilities that links nanoscale mechanisms and microscopic variability to stochastic performance. He noted that many of the simulations used the solid-mechanics finite elements analysis module within the Department of Energy’s Advanced Simulation and Computing code Sierra/SM.7

At the macroscale, Bishop explained, researchers typically perform a component or part analysis and qualification to determine the stress field on the part. AM can follow the same approach, first by determining the complex temperature history at each material point. Then, the as-manufactured state can be calculated using an advanced viscoplastic material model with internal state variables capable of representing processing history (e.g., recrystallization), which may include results relating to the residual-stress field, initial yield stress (field), hardening, and failure. The part performance can then be predicted with error estimation and uncertainty quantification in quantities of interest (Brown and Baumann, 2012).

Bishop highlighted four key challenges and opportunities for computational solid mechanics. The first challenge is whether the concept of a material property is appropriate for AM parts. He emphasized that material property and macrostructure are no longer separable and that the process,

___________________

5 Collaborators include David P. Adams (SNL), John Carpenter (LANL), Ben Reedlunn (SNL), Bo Song (SNL), Todd Palmer (PSU), Jack Wise (SNL), Don Brown (LANL), Bjorn Clausen (LANL), Jay Carroll (SNL), and Mike Maguire (SNL/CA).

6 Collaborators include John Emery, Corbett Battaile, John Madison, Brad Boyce, David Littlewood, Jay Foulk, and Rich Field.

7 The Sierra/SM Theory Manual can be accessed at http://prod.sandia.gov/techlib/access-control.cgi/2013/134615.pdf.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

material, and part must all be qualified concurrently. Assessing the accuracy of homogenization theory for AM materials involves considering scale separation, texture and anisotropy, and surface effects. He said that concepts from a posteriori error estimation need to be applied to quantify errors inherent in homogenization and material-model form error.

Macroscopic homogenization, Bishop explained, is when a complex material with a unique microstructure and fine-scale fluctuations is modeled with mean material behavior. Estimating homogenized material properties is quite involved (Huet, 1990). The first step is to establish a representative volume element (RVE), typically with just a few grains in the smallest case. Displacement, periodic, and traction boundary conditions are then applied to the RVE to compute the apparent property. This step is then repeated with incrementally increased RVEs and eventually the apparent property values with the different boundary conditions converge to a deterministic effective value. Bishop explained that the complex microstructure associated with AM often means that larger RVEs are needed with uncertainty quantification estimates.

He gave an example of direct numerical simulation of multiscale modeling of an I-beam, where an equiaxed grain structure is modeled directly within the engineering-scale finite element model. This model uses crystal-plasticity material models for each grain and can incorporate as-manufactured states (e.g., texture, residual stress), but it requires a massively parallel finite element framework. He showed the von Mises stress field for both the homogenization solution and the multiscale modeling with direct numerical simulation. The results are qualitatively similar but with less detail in the homogenization solution. He then compared these results with an idealized LENS microstructure, showing additional variation. Bishop highlighted that Kinetic Monte Carlo8 simulations can be used to generate the AM microstructures (as shown by T. Rodgers, J. Madison, and V. Tikare at SNL), which can be used to model the melt pool velocity and the shape of the hot zone trailing the melt pool’s path.

The second issue he raised is that the residual-stress field must be quantified with its uncertainty. While he did not discuss this in much detail, he commented that there are many instances of this uncertainty quantification not being done. The residual stress field is often incorrectly assumed to be negligible and this can impact part behavior, especially for AM.

___________________

8 The website for the SPPARKS Kinetic Monte Carlo simulator is http://spparks.sandia.gov//, accessed August 16, 2016.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

The third issue is the use of data science in predictive modeling. He wondered if high-throughput material testing could be utilized for uncertainty quantification, statistical learning, and pattern recognition for material-failure precursors. Also, he suggested that statistical learning, pattern recognition, and emergent behavior could be applied more frequently and more vigorously to AM.

The fourth issue Bishop discussed related to fast simulations for industrial use. Discovery-type simulations are imperative but applying techniques to speed the computation (e.g., reduced-order models) makes the simulations usable for real applications. He emphasized that extremely efficient specialized computational methods are needed. There is an opportunity to break out of current CAD-analysis paradigms to focus on implicit representations of geometry and on implicit representations of approximation spaces so that the meshing process is eliminated (e.g., fictitious-domain methods, finite-cell methods, fast Fourier transform methods [Bishop, 2004], and mesh-free methods). He emphasized again that a posteriori error estimation in engineering quantities-of-interest is needed but heuristics in finite element analysis are still state of the art. In conclusion, Bishop highlighted short- and long-term goals to advance predictive methods in AM. He described the following list of short-term goals:

  • Continue development of advanced viscoplastic macroscopic material models with internal-state variables capable of representing changes to microstructure due to complex processing history;
  • Incorporate process modeling for full-field residual-stress state determination; and
  • Create measurement and inversion techniques for full-field residual-stress state determination.

Bishop also described the following long-term goals:

  • Error estimation in engineering quantities of interest for quantifying material model form error, discretization error, and homogenization error;
  • Process models for microstructure predictions (e.g., KMC, phase field);
  • Multiscale material models that represent microstructure explicitly (e.g., through concurrent homogenization with crystal-plasticity models);
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
  • Development of crystal-plasticity models and advanced calibration methods;
  • Data science enabled by high-throughput testing and digital-volume correlation;
  • Development of implicit geometry representations and computational techniques; and
  • Fast simulations tools for industrial use.

DISCUSSION

Following the three presentations by David Snyder, Gregory Wagner, and Joe Bishop, a panel discussion was held and moderated by Steve Daniewicz. A participant posed a question on how well inclusions can be modeled and if there is the possibility to simulate multiple material powders in the matrix. Snyder commented that thermodynamic predictions are used to define the oxide content and linking this with process modeling could help address geometric questions, but this has not yet been explored. The participant asked if materials can be added for AM, and Snyder commented that his team has focused on the efficacy of precipitation strengthening for aluminum alloys. He said there are many opportunities to advance this strengthening in AM because the rapid cooling and solidification result in unique microstructures that may lend themselves well to strengthening modifications. However, some of the rare oxides that have been observed are large and it is unlikely that they can be worked around solely by strengthening the material. He suspects that there will have to be advances in material processing to help eliminate these defects.

The panel was then asked if AM could be used to grow a single crystal. Snyder commented that there has been a lot of work in dendrite growth theory from the directional solidification and single-crystal growth. Utilizing some of this theory may help, but there are cooling rate and gradient conditions with AM that pose additional challenges.

A participant raised the issue of separating the material models from scales and asked the panel to elaborate on what options were available. Bishop noted that there are anisotropic plasticity models at the macroscale but calibration and material testing is challenging. Scale separation is assumed when using the macroscale plasticity models. He said the method could be applied to a small part without clear separation of scale but the error would have to be quantified.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

An audience member noted that data science approaches are often used in mechanics for linear analysis but asked how applicable these approaches are to nonlinear analysis. Wagner commented that data science has been applied in computer vision, speech recognition, and many other fields, and he believes it could be applied more broadly to nonlinear mechanics. Bishop agreed, noting that data science approaches could help identify correlations that may be precursors to failure, for example. He suggested it is a way to get more out of simulations than is possible using only traditional analysis. Liu commented that data analysis might be a way to accelerate analyses to make simulations more feasible in industry. A participant commented that signal analysis and image analysis approaches could help with pattern matching, and tools are available in other communities that can be applied to mechanics. An audience member emphasized that database management, data compression, pattern recognition, and statistical analyses are all areas that should be examined more.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×

This page intentionally left blank.

Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 33
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 34
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 35
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 36
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 37
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 38
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 39
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 40
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 41
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 42
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 43
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 44
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 45
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 46
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 47
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 48
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 49
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 50
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 51
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 52
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 53
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 54
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 55
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 56
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 57
Suggested Citation:"3 Computational and Analytical Methods in Additive Manufacturing." National Academies of Sciences, Engineering, and Medicine. 2016. Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/23646.
×
Page 58
Next: 4 Monitoring and Advanced Diagnostics to Enable Additive Manufacturing Fundamental Understanding »
Predictive Theoretical and Computational Approaches for Additive Manufacturing: Proceedings of a Workshop Get This Book
×
Buy Paperback | $48.00 Buy Ebook | $38.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

Additive manufacturing (AM) methods have great potential for promoting transformative research in many fields across the vast spectrum of engineering and materials science. AM is one of the leading forms of advanced manufacturing which enables direct computer-aided design (CAD) to part production without part-specific tooling. In October 2015 the National Academies of Sciences, Engineering, and Medicine convened a workshop of experts from diverse communities to examine predictive theoretical and computational approaches for various AM technologies. While experimental workshops in AM have been held in the past, this workshop uniquely focused on theoretical and computational approaches and involved areas such as simulation-based engineering and science, integrated computational materials engineering, mechanics, materials science, manufacturing processes, and other specialized areas. This publication summarizes the presentations and discussions from the workshop.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!