An $$\hbox {FE}^{2}$$ model for the analysis of shape memory alloy fiber-composites.

This contribution deals with a computational model for a shape memory alloy fiber composite. Three main topics have been considered within the presented model. First, a 1D fiber model is derived which accounts for all relevant nonlinear material phenomena of shape memory alloys. These are pseudoelasticity in the high temperature range and pseudoplasticity in the low temperature range. The latter is closely connected to the shape memory effect. The constrained and two-way shape memory effect are captured as well. Second, the shape memory fiber model is implemented into the finite element method. Two different structural elements are derived which lead to two different discretization schemes. A non-conform meshing concept and a conform meshing concept are presented. Randomly oriented and distributed fibers are considered. Both schemes are compared within the paper. Third, an $$\hbox {FE}^{2}$$ ansatz is presented. The computational homogenization process makes the detailed description of the complicated fiber-structure on macro-level dispensable. The micro-structure is considered in a representative volume element. It captures the main characteristics of the multi-functional composite. Finally, numerical examples present the capability of the formulation. [ABSTRACT FROM AUTHOR]