A recursion formula for the integer power of a symmetric second-order tensor and its application to computational plasticity

Abstract

In this paper, a recursion formula is given for the integer power of a second-order tensor in 3D Euclidean space. It can be used in constitutive modelling for approximating failure or yield surfaces with corners, and it is  demonstrated for the case of Rankine failure criterion. Removing corners provides clear advantages in computational plasticity. We discuss the consequences of the approximation errors for failure analyses of brittle and quasi-brittlematerials.