An improvement on the Brinson model for shape memory alloys with application to two-dimensional beam element

In this article, the one-dimensional phenomenological constitutive model originally proposed by Brinson for shape memory alloys is improved to predict asymmetric behavior in tension and compression. We propose an approach that decomposes stress-induced martensite volume fraction into two parts, one in tension and one in compression. Results of numerical examples show reasonable agreement with experimental data. Moreover, we implement the proposed model in a user-defined material subroutine in the nonlinear finite element software ABAQUS/Standard as a two-dimensional Euler-Bernoulli beam element. We simulate several beam problems and a shape memory alloy staple. Regarding the results, the proposed shape memory alloys constitutive model, employed in a two-dimensional beam element, can be used to simulate various shape memory alloys applications in the design and analysis.