A Thermomechanical Model for a One Variant Shape Memory Material

Abstract

A model is examined for thermoelastic materials, such as those that display the shape memory and pseudoelastic effect. As is common with models for these materials, an internal variable is utilized which gives the phase fraction of austenite at the microstructural level within the continua. Evolution equations are developed that govern the time history of the system based on changes in stress, strain and temperature. Hysteresis is inherent in the system due to the Duhem- Madelung form of one of these equations. Attention is focused on the connection between complete transformation phenomena and arrested loading/unloading (outer loops vs. subloops); the transition from isothermal to adiabatic loading via loading in a heat convective environment; the identification of attracting states associated with both temperature cycling and periodic stressing; and the deter mination of mathematical restrictions on otherwise rather general constitutive entities entering the model so as to ensure well-posedness, proper qualitative behavior and admissible thermodynamic behavior.