A model of 3D shape memory alloy materials

Abstract

It is a crucial step how to describe the relationship between the strain, the stress and the temperature field, when we consider the mathematical modelling for shape memory alloy materials. From the experimental results we know that the relationship can be described by the hysteresis operators. In this paper we propose a new system consisting of differential equations as a mathematical model for shape memory alloy materials occupying the three dimensional domain. The key of the modelling is the characterization for the generalized stop operators by using the ordinary differential equations including the subdifferential of the indicator function for the closed interval. Also, we give a proof of the well-posedness of the system.