Tutorial on state variable based plasticity: an Abaqus UHARD subroutine

Abstract

Since plasticity is path dependent, it is necessary to properly take into account the deformation, strain rate and temperature history in applications such as crash worthiness and ballistics simulations. To accurately model the evolution of the yield stress, the incremental (differential) update from a previous converged time step is required instead of a closed form expression that relates flow stress to plastic strain. Elastoviscoplastic models that make use of state variables better capture the physical phenomenon of a perceived lag between a change in strain rate or temperature and the subsequent stress response. It is impossible to capture this when making use of a closed form expression or data table based method. One model that makes use of an evolving state variable is the Mechanical Threshold Stress (MTS) model. In this paper, the implementation of the MTS model into an Abaqus user hardening (UHARD) subroutine is discussed and the code is included. The aim is not to improve on the current knowledge of the model, but to illustrate the ease with which a state variable based plasticity model can be implemented and used instead of an empirical (closed form expression) or data table based method. The MTS model is compared to the Johnson-Cook plasticity model which takes the form of a simple closed form expression relating yield stress to plastic strain as a function of temperature and strain rate. The model parameters are calibrated using isothermal, constant strain rate experimental data and then used to predict the stress response for a strain rate jump test and a temperature change test.