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- W2487511279 abstract "12.1. Introduction. In this chapter, we consider generalizations of the formulations developed in Chapters 2 and 6 to frictionless contact problems involving finite deformations of elastic solids. In addition, we consider an important class of contact problems which involves nonlinear materials and friction: the extrusion of an elastoplastic material through a rigid die.Both of these classes of problems are characterized by highly nonlinear systems of partial differential equations and inequalities for which a complete mathematical basis (i.e., existence theory, regularity theory, etc.) is not yet available. In the case of finite elasticity problems, we are able to establish some existence results within the framework of nonconvex minimization theory, but much remains to be done before adequate mathematical foundations are established for a meaningful regularity and approximation theory. Nevertheless, a reasonable variational framework for these problems can be developed and finite element methods can be constructed which yield physically sound simulations of these types of nonlinear mechanical behavior. The present chapter represents only an introduction to these subjects as a more detailed investigation would not only take us outside the scope of this work but would also require a departure from the systematic approach we have attempted to follow." @default.
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- W2487511279 date "1988-01-01" @default.
- W2487511279 modified "2023-10-16" @default.
- W2487511279 title "12. Contact Problems Involving Deformations and Nonlinear Materials" @default.
- W2487511279 doi "https://doi.org/10.1137/1.9781611970845.ch12" @default.
- W2487511279 hasPublicationYear "1988" @default.
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