Micromechanics and Homogenization of SMA-Wire-Reinforced Materials

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.

Micro–macro analysis of shape memory alloy composites

“…The second technique proposed by Marfia and Sacco (2005) evaluates the quantities E, P, R X and P X solving the problem of periodic composites using the finite element method. Moreover, a numerical micromechanical analysis of a periodic SMA composite is performed, developed suitable finite elements for the fiber and the matrix.…”

“…A homogenization procedure based on the analysis of a periodic composite is proposed and described in detail in Marfia and Sacco (2005). The quantities E, P, R X and P X that characterized the composite response are evaluated by linear finite element analyses.…”

“…Briggs and Ponte Castañ eda (2002) studied the effective behavior of active composites, obtained embedding aligned SMA fibers in a linear elastic matrix, using the homogenization technique proposed by Ponte Castañ eda (1991). Marfia and Sacco (2005) presented a micromechanical study of composite with embedded SMA fiber developing analytical and numerical homogenization procedures in order to determine the overall response of the composite.…”

Numerical homogenization techniques for the evaluation of mechanical behavior of a composite with SMA inclusions

“…Recently, works by Marfia and Sacco [2005] and Marfia [2005] were published, concerning micromechanical modeling of SMA-wire-reinforced materials. The authors proposed two homogenization procedures based on the following assumptions: the martensite volume fraction depends on the wire temperature and only on the normal stress acting in the fiber direction, and the inelastic strain occurs along the fiber direction.…”

A Homogenization Technique for Elasto-Plastic Composites

“…This technique takes into account the nonlinear behavior of the constituents, introducing an approximation of the inelastic strain. In the literature, several TFA schemes have been developed, differing mainly in the assumption concerning the distribution of the inelastic strain and in the computation of the internal variable evolution [2,3,4,5,6].…”