Theoretical and numerical modeling of dense and porous shape memory alloys accounting for coupling effects of plasticity and transformation

The present work develops three-dimensional phenomenological constitutive models for dense and porous shape memory alloys (SMAs). The models are extensions of a recent work and considers pressure dependent behavior for porous SMAs as well as the coupling effects of transformation and plasticity for both dense and porous SMAs. In contrast to dense SMAs, a considerable plastic strain accumulates in porous SMAs even during phase transformation. Therefore, an effective solution algorithm for simultaneous evolution of transformation and plastic strain is presented via replacement of the classical Kuhn-Tucker inequality conditions by the so-called Fischer-Burmeister complementarity function. Numerical predictions are compared with experimental results and a comprehensive study is performed on the material parameters regarding coupling effects and pressure dependency. Moreover, we implement the model using corotational formulation and perform finite element analysis of a porous SMA spring actuator, and a tube under non-proportional loading to assess the reliability of the proposed model for large rotations and general multiaxial loadings.