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.

Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys

“…Beams manufactured from shape memory alloys have been intensively investigated due to their superb actuation and energy harvesting capabilities [42][43][44]. Although analytical models can be very useful for quick concept validation and preliminary design studies [45][46][47], full-scale FEM simulations are often indispensable in detailed studies [42,44,48,49], since they are not constrained by assumptions on a particular geometry, material response, boundary conditions, etc. The simulated problem mimics a simple beam with a rectangular cross-section (with its width being half of the height) loaded at both ends and supported in the middle so that bending is invoked.…”

“…Reformulation of the models within the finite strain (large deformation) theory poses another challenge, both from the modeling and from the implementation (vectorization) points of view. Inspiring attempts involving these aspects have been carried out (e.g., in [13,48,57]).…”