TABLE OF CONTENTS The theory of elastoplastic media is now a mature branch of solid and structural mechanics, having experienced significant development during the latter half of this century. In particular, the classical theory, which deals with small-strain elastoplasticity problems, has a firm mathematical basis, and from this basis further developments, both mathematical and computational, have evolved. Small-strain elastoplasticity is well understood, and the understanding of its governing equations can be said to be almost complete. Likewise, theoretical, computational, and algorithmic work on approximations in the spatial and time domains are at a stage at which approximations of desired accuracy can be achieved with confidence.
The finite-strain theory has evolved along parallel lines, although it is considerably more complex and is subject to a number of alternative treatments. The form taken by the governing equations is reasonably settled, though there is as yet no mathematical treatment of existence, uniqueness, and stability analogous to those of the small-strain case. Computationally, great strides have been made in the last two decades, and it is now possible to solve highly complex problems with the aid of the computer.
This monograph focuses on theoretical aspects of the small-strain theory of elastoplasticiy with hardening assumptions. It is intended to provide a reasonably comprehensive and unified treatment of the mathematical theory and numerical analysis, exploiting in particular the great advantages to...
