Numerical technique in plasticity including solution advancement control

Abstract

Numerical techniques applied to the consistent formulation of plasticity, which is based on convex analysis, are investigated. For each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses, while the velocity field is the extremal of a non‐quadratic functional. Explicit formulas for von Mises' yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved, for comparison, by a number of Newton‐type iteration procedures with line search and are‐length control. A few numerical examples with proportional and non‐proportional loading are analyzed.