A recursive calculation of the consistent tangent operator in elasto-plasticity

Abstract

The paper presents a derivation of the consistent tangent operator (CTO) for the class of iterative constitutive integration algorithms. The derivation is based on a variational analysis of algorithmic equations with respect to the strain dependency of state variables in each iteration. Such treatment results in a recursive formulation, where the value of CTO is updated based on its old value. The proposed formulation is demonstratively applied to the cutting-plane algorithm (CPA), for which it is known that a closed form solution for CTO does not exist.