A nonlinear finite element method applied to shape memory bars

摘要

This contribution is concerned with the analysis of the nonlinear behavior of shape memory bars, employing the finite element method. A constitutive equation based on Fremond's theory is considered. The proposed constitutive model considers four phases in the formulation (three variants of martensite and an austenitic phase), including thermal expansion and plastic strains. An iterative numerical process based on an operator split technique is developed in order to deal with the nonlinearities of the formulation. On this basis, coupled governing equations can be solved from uncoupled problems where classical procedures can be employed. Numerical simulations are carried out in order to illustrate the general behavior of shape memory bars under different thermomechanical loadings. Results show that the proposed model captures the general behavior of SMAs, allowing the description of bars subjected to non-homogeneous thermomechanical loads.