The Model of Hysteretic Behavior of SMA Based on the High Order Approximation of Differential Equation Method

Abstract
Due to thermomechanical hysteresis in solids undergoing martensitic type of structure transformations the macroscopic strain and volume fraction of martensite are not a single-valued function of stress and temperature, but they become functions of the process of their change. Some of the phenomenological approaches describing main thermomechanical properties of shape-memory alloys (SMA) connected with hysteresis were recently developed. A special type of differential equations (DE) describing evolution of the inelastic macroscopic strain and volume fraction of martensite as functions of the temperature have been proposed in our recent papers. Simplest applications of these equations to a strain evolution during the multiple temperature cycling in a small temperature interval have been also discussed. Some other problems associated with the irreversible processes caused by hysteresis will be discussed in the present paper. In particular, a new interpretation of DE method based on the transition probability concept and high order approximation including the return point effect is considered.