Research Directions in Computational Mechanics (1991)

The manufacture of material products involves many unit processes that alter the external form and surface as well as the interior structure of the material components and final assembly. These include such processes as grinding, melting, chemical processing, atomizing, agglomerating, casting, molding, thermal processing, deformation processing, forming, machining, coating, and joining. From a scientific viewpoint, these processes involve such subjects as fracture mechanics, heat transfer, fluid mechanics, electromagnetodynamics, chemical reactions, solid mechanics (especially plasticity), and metallurgical reactions. In the past these subjects have been useful as qualitative guides for the design and development of various manufacturing processes, but such activities have progressed primarily by empirical trial and error.

Today, the subject of design and development of manufacturing processes is undergoing a dramatic revolution. There is a long way to go, but the direction is increasingly clear. Physically realistic mathematical simulations of unit processes are being developed. Increasingly, these simulations are being used to replace many of the physical trials that were necessary in the past. The times and costs of process development are being reduced. The final designs are better because they are based in quantitative physical science. The vision is a physical-science-based, mathematically expressed design methodology that can be used by manufacturing engineers to create designs of manufacturing processes with the same confidence that structural engineers now use elasticity-based methods to create designs of bridges and buildings.

The mathematical expressions of manufacturing processes are considerably more complex than those of elastic structures, and the processes are often inherently three-dimensional and nonsteady. Yet the development of large-scale computers has now brought the exercise of these mathe-

matical simulations within reach, and it is clear that further development of computer hardware and software will render them increasingly available. The issue of feasibility is past.

Mathematical expressions of manufacturing processes involve the classical physical laws of conservation of mass, energy, and momentum. They also involve constitutive relations describing the physical response of particular materials. Specific process simulations are obtained by applying specific boundary conditions to the resulting (usually quasi-linear) partial differential equations. The boundary conditions themselves often must be constitutive, describing the surface behavior of the materials being pressed and the tools being utilized. Because the physical nature of the materials being processed is often changed by the process, the constitutive equations (both interior and boundary) must involve not only state equations expressing, say, the relationship of deformations to stresses and temperatures in the current material state but also evolution equations expressing how the material state is changing.

Development of the constitutive equations for manufacturing processes is itself a rich field for computational mechanics. Such constitutive equations can be developed empirically by fitting data from many carefully controlled laboratory experiments. Increasingly, however, the development of these equations is also being guided by micro-mechanical models that idealize the microstructure of the materials being processed and calculate the response of idealized structures to various thermomechanical responses to create the macroscopic constitutive relations. This leads directly to constitutive relations with dependent variables representing specific microstructural features. In fact, it is now becoming possible to develop macroscopic constitutive equations based on a hierarchy of increasingly fine substructural scales, reaching from featureless continua to atomic structures. This is an extremely rich area for the integration of computational mechanics, materials science, and solid-state physics.

These complex and physically detailed constitutive relations provide a rich basis for concurrent design of materials and their processes, but such detail is usually unnecessary for good design of a process for a particular material. In fact, it is often desirable, because of the computational simplification that can be achieved, to perform preliminary design with the simplest possible constitutive models such as Newtonian fluids, linear hypoelastic solids, and rigid/perfectly plastic solids. Then final designs can be achieved by iteration about the preliminary design using increasingly complex models.

To summarize, a revolution is occurring in the way manufacturing processes are being designed and developed. Costly and time-consuming empirical methods of the past are being replaced by more accurate, less costly, and faster physical-science-based computer simulations. The material aspects of the computer simulations are contained in constitutive equations that describe the evolution of the material as well as its current response. Development of the constitutive equations as well as the full process simulation involves computational mechanics. Simple constitutive equations are advocated for preliminary process design and more detailed equations for fine tuning.

Permission to reproduce some figures in this document was given by the following:

1. Pergamon Press, New York, N.Y., Figs. 6.1 and 6.2 from and 1988 and 1989.

2. Elsevier-Science Publishers, Amsterdam, The Netherlands, Fig. 6.3 from Mechanics Materials, Vol. 6, 1987.

3. Fig. 6.4; Innovations in Ultrahigh-Strength Steel Technology, Proceedings of the 34th Sagamore Army Materials Research Conference, (ed. by G.B. Olson, M. Azrin, and E.W. Wright), pp. 3–66.

4. Kluwer Academic Publishers, Amsterdam, The Netherlands, Fig. 6.5 from International Journal of Fractures, 1988.

5. Lawrence Livermore National Laboratory, Fig. 13.1 and Fig. 13.2, 1988.