Asymptotic numerical method for finite plasticity

Abstract

This paper discusses the efficiency of an algorithm based on the Asymptotic Numerical Method (ANM) to solve large strain plasticity problems. In the framework of ANM, the non-smooth constitutive law has to be replaced by a smooth one in order to be able to represent the solution path in the form of Taylor series. For this purpose, we propose to generalize the approach used in the small strain case. To achieve this, we introduce a regularized stress–strain relation that considers smoothed elastic–inelastic transitions. This regularized law is a relationship between two scalars, namely the yield function and the plastic multiplier. Classical uniaxial traction benchmarks permit to assess the procedure and to adjust the parameters of the algorithm: regularization parameters, truncation orders and parametrization. • This paper discusses the efficiency of an algorithm based on the Asymptotic Numerical Method (ANM) to solve large strain plasticity problems. • The non-smooth constitutive law has to be replaced by a smooth one in order to be able to represent the solution path in the form of Taylor series. • Classical uniaxial traction benchmarks permit to assess the procedure and to adjust the parameters of the algorithm.