Modeling of shape memory alloy shells for design optimization

A three-dimensional phenomenological constitutive model for the analysis and design optimization of shape memory alloy (SMA) structures is presented. This model specifically targets the pseudoelastic behavior due to the R-phase transformation in NiTi alloys, but also applies to similar SMA materials with low hysteresis. A history-independent formulation is presented, which allows cost-effective sensitivity analysis. The possibility to efficiently compute design sensitivities is essential for enabling the use of gradient-based optimization algorithms, which will allow design optimization of complex SMA structures. The use of the constitutive model in a problem of realistic complexity is illustrated by the analysis of a SMA miniature gripper, modeled using shell elements. The sensitivity analysis of SMA structures using the presented model is addressed in an accompanying paper. Keywords: Shape memory alloys; Pseudoelasticity; NiTi; Constitutive modeling; R-phase; History-independence