A coupled layered thermomechanical shape memory alloy beam element with enhanced higher order temperature field approximations

This article describes the development and validation of a new thermomechanically coupled multi-layered shape memory alloy beam finite element. The finite element is formulated, assuming coupled equilibrium equations for the mechanical and thermal problems. The constitutive shape memory alloy model of Lagoudas and coworkers is implemented in the formulation. Multi-field kinematic hypotheses are proposed, combining a first-order shear displacement field with a sixth-order polynomial temperature field through the thickness of the beam, enabling adequate representation of the temperature and phase transformation profiles due to rapid thermal loading, uneven thermal loading, and boundary conditions and multi-layered configurations with variable thermal properties. The non-linear transient discretized equations of motion of the shape memory alloy beam are synthesized and solved using the Newton–Raphson method with an implicit time integration scheme. Numerical results illustrate the time response of uniform and bi-layered NiTi beams under various thermomechanical loads predicted by the developed finite element. Correlations of the beam element predictions with those of plane stress two-dimensional finite element shape memory alloy models demonstrate excellent agreement in the calculated displacement, temperature, and phase transformation fields. Additionally, the developed beam finite element yields computationally fast simulations providing an effective tool for the design and simulation of rod, beam, and strip shape memory alloy actuators and active structures.