Transformation and Plasticity of Shape Memory Alloy Structures: Constitutive Modeling and Finite Element Implementation

In this work, we extend a well-known three-dimensional phenomenological shape memory alloy (SMA) constitutive model known as Souza model. The proposed model describes more precisely the hardening behavior observed during forward- and reverse-phase transformation as well as evolution of plastic strain and its effects on transformation behavior. Moreover, we present a solution algorithm for low temperatures and evolution of plastic strains which considerably reduces the computational cost. Through calibration of material parameters, the model is able to predict pseudo-elasticity and shape memory properties of SMAs more accurately compared to Souza model. Moreover, the plasticity and its effect on transformation are well predicted by the proposed model. Through finite element implementation, we can perform simulations on complex SMA structures. Finally we compare the run time for the present algorithm with the iterative Newton method used for solving equations of Souza model. The comparisons show that the computational cost of the proposed algorithm is considerably lower than previous algorithms.