CONVERGENCE OF FINITE-ELEMENT METHOD FOR A CLASS OF ELASTIC-PLASTIC SOLIDS

A proof of convergence of the finite-element method in rate-type, quasi-static boundary value problems is presented. The bodies considered may be discretely heterogeneous and elastically anisotropic, their plastic behavior governed by history-dependent, piecewise-linear yield functions and fully coupled hardening rules. Elastic moduli are required to be positive-definite and plstic moduli nonnegative-definite. Precise and complete arguments are given in the case of bodies whose surfaces are piecewise plane.