Multi-dimensional superelastic behavior of shape memory alloys via nonlinear finite element method

This paper presents a methodology for the simulation of multi-dimensional nonlinear thermomechanical behavior of shape memory alloys by the finite element method. The numerical multi-dimensional constitutive model is formulated by thermomechanics incorporated with the “yield” (transformation start stress in stress induced martensitic transformation) surface of shape memory alloys. In this formulation, the phase flow direction can be decided by using the “yield” stresses of a particular SMA in uni-axial tension and compression. The solution of the geometrically and physically nonlinear problem is achieved using Newtonʹs iteration method. Numerical results for the uniaxial model, three and four-point bending tests and smart composite embedded with shape memory alloys show that the proposed procedure is an effective computational tool for the simulation of a broad range of applications based on shape memory materials.