Shape memory alloys: Micromechanical modeling and numerical analysis of structures

Multiscale modeling of structures made from shape memory alloys (SMA) is pr esented. Starting with consideration of a single transformation event at th e micro-level and averaging over the representative volume, micromechanical ly-based macroscopic constitutive equations are derived, which are used in Finite Element Method (FEM) code to model the behaviour of structures. Usin g the thermodynamic theory of phase transformations (PT) in elastic materia ls on the micro-level, the macroscopic associated transformation flow rule, the corresponding extremum principle and the nonconcavity of the transform ation surface are derived for transformational micromechanisms of inelastic deformation due to phase transformation, twinning and reorientation of mar tensitic 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 J(2)-plasticity theory. It allows one to m odify the FEM for elastoplasticity (including the radial return algorithm f or numerical integration of the constitutive equations and calculation of t he consistent tangent moduli) in order to model PT in SMA. Some axisymmetri c problems for PT in SMA tubes are solved. In particular, PT regularities o f a tube assembly with a SMA cylinder element are investigated at different external conditions.