Phase transformation in shape memory alloys: a numerical approach for thermomechanical modeling via peridynamics

The work is devoted to the numerical aspects of the modeling tool elaborated to simulate the phenomenon of solid phase transformation in shape memory alloys. Particularly, a nonlocal approach, namely the bond based variant of peridynamics, is of concern to handle material model nonlinearities conveniently. The proposed model considers thermomechanical coupling which governs kinetics of the process of phase change. The phenomenological peridynamic model of a shape memory alloy is based on the Gibbs free energy concept and thermoelasticity. The work focuses on the superelasticity effect which can be observed when a tested material is subjected to a mechanical load. As a demanded application scope for the proposed smart material model, its scheduled future use in the study of operational conditions for a gas foil bearing is considered. The motivation of the work has primarily originated from the perspective of more accurate, i.e., more physical, modeling of the structural components which employ shape memory alloys to stabilize the bearing operation. The authors conduct a preliminary investigation regarding the properties of the newly proposed numerical multiphysics approach. Specifically, the scope of the work covers description of the developed computational framework as well as detailed derivation of its stability criteria. Exemplary numerical results complement the paper providing with determination of the stress–strain relation and adequate parametric study.