A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field

The present paper deals with a homogenization technique based on the Transformation Field Analysis (TFA) for the study of heterogeneous composite media characterized by nonlinear response. According to the TFA, the behavior of the representative volume element (RVE) is studied accounting for the nonlinear effects by means of the presence of a uniform inelastic strain distribution in the nonlinear constituent of the heterogeneous material. In order to improve the TFA, the assumption of uniformity of the inelastic strain distribution is removed, so that a nonuniform inelastic strain field, better representing the inelasticity distribution in the composite, is considered. In particular, the inelastic strain is represented as a piecewise linear combination of analytical functions of the spatial variable. The theory, presented in a general framework, can be successfully adopted for deriving the overall constitutive response for a wide range of nonlinear composite materials. Furthermore, the procedure is tailored to investigate the response of composites whose constituents are Shape Memory Alloys (SMA) and materials characterized by plastic behavior. Finally, numerical applications are developed in order to assess the effectiveness of the proposed nonuniform TFA procedure, comparing the results with the ones carried out performing Uniform and Piecewise Uniform TFA homogenizations and nonlinear finite element micromechanical analyses.