Evaluation of a Constitutive Model for Shape Memory Alloys Embedded in Shell Structures

The evaluation of a phenomenological three-dimensional constitutive model for shape memory alloys embedded in shell structures is presented. The constitutive model, originally proposed by Graesser and Cozzarelli, provides the capability to model both the martensitic twinning hysteresis and martensite-austenite superelastic behavior typical of shape memory alloys. This is achieved by casting the parameters used to define the behavior of the model in a temperature dependent form. The model is formulated using strain rate dependence to define the inelastic strain response of the shape memory alloy. The proposed three-dimensional equations are recast in the form of generalized plane stress for use with shell elements. Implementation of the model within a shell based finite element code is reviewed. The constitutive model was formulated as strain rate dependent, and was implemented using the concepts of endochronic plasticity resulting in an incremental form suitable for rate independent finite element analysis. Simulations of a passive vibration isolator consisting of a composite leaf-spring laminated with shape memory alloy foils are detailed. The vibration isolator is designed to dissipate energy by taking advantage of the shape memory alloy's stress induced martensite twinning hysteresis activated by bending of the leaf-spring arrangement. Adaptivity of the isolator is demonstrated using the shape memory effect to change from the passive isolation mode to a stiffer austenitic configuration via the shape memory effect. Isolation is intended for relatively large amplitude and low frequency excitation. A number of geometrical design alternatives are investigated using materially and geometrically non-linear finite element simulations. Results of the analyses show that large amounts of passive damping can be obtained using the laminated leaf spring arrangement.