SUMMARYThe aim of the present paper is to propose a phenomenological thermodynamically consistent 3D model for shape memory alloys (SMA) in the finite strain range. In particular, a model able to predict the main features of SMA materials, such as the superelastic and the shape-memory effects, is proposed. The model is based on the assumption of the local multiplicative split of the deformation gradient into an elastic and a phase transformation part. The governing state and evolutive equations are written in the undeformed configuration. The material parameters of the model are characterized by a clear physical meaning so that they can be determined by simple experimental tests. The finite deformation SMA model is also reformulated in the framework of small strain, linearizing the strain and stress measures in order to obtain a consistent constitutive model preserving the nonlinear material response. A robust algorithm is adopted in order to integrate the nonlinear evolutive equations; 2D and 3D finite elements are implemented in a numerical code considering finite and small deformations. Some numerical applications are carried out showing the performances of the proposed model and the developed numerical procedure to describe the superelastic and the shape-memory effects of SMA devices. Comparisons of different results obtained by the small and finite strain formulations are reported.

The paper deals with the modeling and the development of a numerical procedure for the analysis of shape-memory alloy (SMA) elements in order to predict the main features of SMA devices. A 3D SMA model in the framework of small strain theory is developed starting from the thermo-mechanical model proposed by Souza et al. (Eur J Mech A/Solids 17:789-806, 1998) and modified by Auricchio and Petrini (Int J Numer Methods Eng 55: 2002). The aim of this paper is to propose some more modifications to the original model, to derive its consistent 1D formulation, to clarify the mechanical meaning of the material parameters governing the constitutive model. A robust time integration algorithm is developed in the framework of the finite element method and a new beam finite element is proposed. Some numerical applications and a comparison with experimental data available in literature are carried out in order to assess the ability of the proposed model to describe the SMA behavior.

No abstract

The aim of the paper is to develop a micromechanical model for the evaluation of the overall constitutive behavior of a composite material obtained embedding SMA wires into an elastic matrix. A simplified thermomechanical model for the SMA inclusion, able to reproduce the superelastic as well as the shape memory effect, is proposed. It is based on two assumptions: the martensite volume fraction depends on the wire temperature and on only the normal stress acting in the fiber direction; the inelastic strain due to the phase transformations occurs along the fiber direction. The two introduced hypotheses can be justified by the fact that the normal stress in the fiber direction represents the main stress in the composite. The overall nonlinear behavior of long-fiber SMA composites is determined developing two homogenization procedures: one is based on the Eshelby dilute distribution theory, the other considers the periodicity conditions. Numerical applications are developed in order to study the thermomechanical behavior of the composite, influenced by the superelastic and shape memory effects occurring in the SMA wires. Comparisons of the results obtained adopting the two homogenization procedures are reported. The influence of the matrix stiffness and of a prestrain in the SMA wires on the overall behavior of the composites is investigated.

No abstract