Microstructural modeling of a TiNi beam bending

This work presents a numerical simulation of a TiNi shape memory alloy (SMA) beam deformation in the mode of pure bending. The beam is loaded by a bending moment and experiences temperature variations. The boundary-value problem includes the equations of the mechanical equilibrium and the constitutive relations of the SMA realized by a microstructural model, which accounts for the strains due to elasticity, thermal expansion, and phase transformation. Bending at different temperatures and the shape recovery on heating are simulated. Thickness distributions of the stress and dependences of the deflection on the bending moment and temperature are obtained. Since the microstructural model automatically accounts for the tension-compression asymmetry of TiNi its use for the description of the SMA behavior predicts that the neutral line of the bent beam does not pass through its center.