A thermomechanical finite strain shape memory alloy model and its application to bistable actuators

Abstract

This work presents a thermomechanical finite strain shape memory alloy model that utilizes a projection method to deal with the incompressibility constraint on inelastic strains. Due to its finite strain formulation, it is able to accurately predict the behavior of shape memory alloys with high transformation strains. The key feature of this model is the thermomechanical modeling of the shape memory effect and superelastic behavior by optimizing a global, incremental mixed thermomechanical potential, the variation of which yields the linear momentum balance, the energy balance, the evolution equations of the internal variables as well as boundary conditions of Neumann- and Robin-type. The proposed thermal strain model allows to properly capture transformation induced volume changes, which occur in some shape memory alloys. A finite strain dissipation potential is formulated, which incorporates the disappearance of inelastic strains upon austenite transformation. This important property is consistently transferred to the time-discrete potential using a logarithmic strain formulation. Yield and transformation criteria are derived from the dual dissipation potential. The implementation based on an active set search and the algorithmically consistent linearization are discussed in detail. The model is applied in three-dimensional simulations of a bistable actuator design to explore its capabilities.