Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort resolve. Finite methods, which rely on Gauss quadrature integration schemes, must solve two sets coupled differential equations: one at the global level and other local, i.e. point level. In contrast conventional return mapping algorithm, solves these equations separately using nested Newton procedure, we propose scheme local simultaneously. process also derive closed-form expressions used update internal/constitutive state variables, unify popular closest-point cutting plane methods with our formulas. Numerical testing indicates method allows larger thermomechanical loading steps provides increased efficiency, over standard algorithm.