Finite element analysis of a class of problems in finite elastoplasticity based on the thermodynamical theory of materials of type N. (Q801724)

This paper describes a finite element approximation scheme for computing finite elastoplastic deformations of a hypothetical class of materials referred to as materials of type N. Kinematical descriptions of motion and strain-rate and rotationally invariant stress-rates measures appropriate for finite elastoplastic deformations are derived and the thermodynamical theory for materials of type N is briefly reviewed. Finite element approximations of the governing nonlinear equations are derived along with numerical algorithms for solving the associated discrete nonlinear system. These new methods are applied to some representative plane-strain problem, including problems with unloading and reloading and the problem of upsetting of a partially constrained rectangular billet.