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An incremental form of constitutive model is proposed for shape memory alloys using the modified strain based on experimental results and the finite element analysis, taking into account of the laminar microstructure, the thickness of martensite phase lamina and the interaction between the two phases. The pseudoelastisity of NiTi shape memory alloy micro-tube subjected to pure tension and pure torsion are analyzed and compared with the experimental results respectively. It can be seen that the pseudoelastic behavior, especially the stress drop during tension processes, can be well described with the proposed model.

A pearlitic steel is composed of numerous pearlitic colonies with random orientations, and each colony consists of many parallel lamellas of ferrite and cementite. The constitutive behavior of this kind of materials may involve both inherent anisotropy and plastic deformation induced anisotropy. A description of the cyclic plasticity for this kind of dual-phase materials is proposed by use of a microstructure-based constitutive model for a pearlitic colony, and the Hill's self-consistent scheme incorporating anisotropic Eshelby tensor for ellipsoidal inclusions. The corresponding numerical algorithm is developed. The responses of pearlitic steel BS11 and single-phase hard-drawn copper subjected to asymmetrically cyclic loading are analyzed. The analytical results agree very well with experimental ones. Compared with the results using isotropic Eshelby tensor, it is shown that the isotropic approximation can provide acceptable overall responses in a much simpler way.

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