How to simplify return-mapping algorithms in computational plasticity: part 1 - main idea

Abstract

An improved implicit return-mapping scheme for nonsmooth yield surfaces is suggested in this paper. It is based on a subdifferential formulation of the flow rule that does not require special treatment at singular points (apices, edges, etc.). Although the flow direction is multivalued in such a case, it is shown that the suggested scheme leads to solving a unique system of nonlinear equations similarly as for smooth yield surfaces. Improved return-mapping schemes of several elastoplastic models containing nonassociative plastic flow rules and nonlinear isotropic hardening laws are introducedtogether with the corresponding consistent tangent operators.