Finite element analysis of a shape memory alloy three-dimensional beam based on a finite strain description

In the present work a modified phenomenological model of the shape memory alloy (SMA) constitutive law is proposed that is capable of reproducing some aspects of SMA thermomechanical behavior like superelasticity and the one-way shape memory effect. The modified law uses strain and temperature as control variables, which eliminates the need for transformation correctors in finite element analysis. It is implemented in a structural model developed to analyze three-dimensional (3D) structures made out of thick beam elements with features such as taper and curvature, given that SMA products typically fall in this category of shapes. Moreover, a finite strain and large displacement description is adopted to account for the large deformations exhibited during phase transformation. Results, produced by the proposed model, of simulated tensile, three-point and four-point bending tests are presented and compared with experimental data taken from the literature.