Stress–strain measures used in the ANSYS package to solve elastoplastic problems at finite strains

Abstract

It is shown that the Dienes (or the Green–McInnis–Naghdi) derivative is used in the ANSYS package rather than the Jaumann derivative as an objective derivative for the Cauchy stress tensor when solving elastoplastic problems, although the usage of the Jaumann derivative is stated in the ANSYS theory reference manual. In this manual it is also stated that, for these problems, the strain tensor is the Hencky logarithmic strain tensor; however, in reality, this strain tensor is the right nonholonomic strain tensor such that the left nonholonomic strain tensor associated with the right one is generated by the Dienes derivative.