Plasticity: Mathematical Theory and Numerical AnalysisThe 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. This monograph focuses on theoretical aspects of the small-strain theory of hardening elastoplasticity. 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 be gained by placing the theory in a convex analytic context. The book is divided into three parts. The first part provides a detailed introduction to plasticity, in which the mechanics of elastoplastic behavior is emphasized. The second part is taken up with mathematical analysis of the elastoplasticity problem. The third part is devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. The work is intended for a wide audience: this would include specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory. |
Contents
Continuum Mechanics and Linear Elasticity | 15 |
Elastoplastic Media | 41 |
The Plastic Flow Law in a ConvexAnalytic Setting | 71 |
Results from Functional Analysis and Function Spaces | 97 |
Variational Equations and Inequalities 125 | 124 |
The Primal Variational Problem of Elastoplasticity | 151 |
The Dual Variational Problem of Elastoplasticity 177 | 176 |
Introduction to Finite Element Analysis | 205 |
Approximation of Variational Problems | 223 |
Approximations of the Abstract Problem | 237 |
Numerical Analysis of the Primal Problem | 271 |
Numerical Analysis of the Dual Problem | 319 |
355 | |
365 | |
Other editions - View all
Plasticity: Mathematical Theory and Numerical Analysis Weimin Han,B. Daya Reddy Limited preview - 1999 |
Plasticity: Mathematical Theory and Numerical Analysis Weimin Han,B. Daya Reddy No preview available - 2014 |
Plasticity: Mathematical Theory and Numerical Analysis Weimin Han,B. Daya Reddy No preview available - 1999 |
Common terms and phrases
analysis assume assumptions Banach space behavior bilinear form boundary value problem bounded components constant convergence convex defined deformation denote derive domain DUAL1 elastic elasticity tensor elastoplasticity elastoplasticity problem elliptic variational equation equivalent example exists finite element method finite element space flow law fully discrete Hilbert space inner product internal variables isotropic hardening kinematic and isotropic Lemma linear functional Lipschitz continuous material nonnegative normed space numerical obtain order error estimates piecewise plastic strain polynomial primal variational Problem ABS problem DUAL proof regularity relation result satisfies scalar schemes second-order tensor Section sequence Sobolev Sobolev spaces solution algorithms stress subset symmetric Theorem theory time-discrete unique solution v v e V-elliptic variational inequality variational problem vector weak formulation yield function yield surface