SMA Pseudoelastic Finite Strains. Theory and Numerical Application

A tridimensional finite element model of isothermal pseudoelastic deformations is proposed in order to analyze and predict the behavior of shape memory alloys (SMA). To perform finite strain calculations, the mechanical modeling is based on a formulation in a non material rotating frame. The constitutive equations in a particular configuration are closed form of those developed with small strain assumption. This leads naturally to a numerical scheme composed of an elastic prediction and a possible pseudoelastic correction. To insure the convergence of the equilibrium equation solving method, a consistent tangent operator with the stress calculation algorithm is defined. In the case of thin structures, the proposed model is consistent with the zero normal stress condition within a three node shell element based on a mixed interpolation in order to avoid transverse shear locking. Numerical results are presented to show the accuracy of the proposed approach.