Shape memory alloys: Micromechanical modeling and numerical analysis of structures

Multiscale modeling of structures made from shape memory alloys (SMA) is presented. Starting with consideration of a single transformation event at the micro-level and averaging over the representative volume, micromechanically-based macroscopic constitutive equations are derived, which are used in Finite Element Method (FEM) code to model the behaviour of structures. Using the thermodynamic theory of phase transformations (PT) in elastic materials on the micro-level, the macroscopic associated transformation flow rule, the corresponding extremum principle and the nonconcavity of the transformation surface are derived for transformational micromechanisms of inelastic deformation due to phase transformation, twinning and reorientation of martensitic variants. A simple three-dimensional micromechanically-based model for thermoelastic martensitic PT is presented. The model is transformed to the fashion similar to that for J₂-plasticity theory. It allows one to modify the FEM for elastoplasticity (including the radial return algorithm for numerical integration of the constitutive equations and calculation of the consistent tangent moduli) in order to model PT in SMA. Some axisymmetric problems for PT in SMA tubes are solved. In particular, PT regularities of a tube assembly with a SMA cylinder element are investigated at different external conditions.