Consistent derivation of non-constant material function for one-dimensional shape memory alloy phenomenological model

Abstract

Constitutive modelling of shape memory alloys with new material functions is presented within the frame work of thermodynamic consistency. A one- dimensional constitutive model based on the previous work of constant and non-constant material functions is redefined from first principles. In the first step Clausius-Duhem inequality condition for stress is rewritten and an alternate form of differential equation is proposed. The initial and final condition of evolution are applied to obtain a new form of non-constant transformation tensor, which is independent of residual strain the SMA material. As a result in the present work the residual strain is purely defined as a function of transformation stress and not as a function of transformation modulus. The proposed form of new transformation tensor is compared with previously proposed material function and validation results for the consistency are presented. It is observed that newly derived non-constant material function is compatible in both differential and integrated form of the one-dimensional shape memory alloy constitutive relation and satisfies the evolution conditions of phase transformations.