SUMMARYPrevious studies by the authors and their co-workers show that the structure of equations representing shape Memory Alloy (SMA) constitutive behaviour can be very similar to those of rate-independent plasticity models. For example, the Boyd-Lagoudas polynomial hardening model has a stress-elastic strain constitutive relation that includes the transformation strain as an internal state variable, a transformation function determining the onset of phase transformation, and an evolution equation for the transformation strain. Such a structure allows techniques used in rate-independent elastoplastic behaviour to be directly applicable to SMAs. In this paper, a comprehensive study on the numerical implementation of SMA thermomechanical constitutive response using return mapping (elastic predictor-transformation corrector) algorithms is presented. The closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm, an explicit scheme already presented in an earlier work. The closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the ow rule and the inversion of the algorithmic tangent tensor. A uniÿed thermomechanical constitutive model, which does not take into account reorientation of martensitic variants but uniÿes several of the existing SMA constitutive models, is used for implementation. Remarks on numerical accuracy of both algorithms are given, and it is concluded that both algorithms are applicable for this class of SMA constitutive models and preference can only be given based on the computational cost.

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Editor's Note: A hypertext-enhanced version of this article is available on-line at www.tms.org/pubs/journals/JOM/0503/ Combining structure and battery (power) functions in a single material entity permits improvements in system performance not possible through independent subsystem optimizations. The design of composite multifunctional materials for optimal system performance involves selection of constituents, material architecture, and interface connections. This overview focuses primarily on plastic lithium-ion structure-battery materials. Three main topic areas are considered: rules and tools for analysis and design of multifunctional materials; multifunctional structure-battery material systems; and structure-battery in the Defense Advanced Resources Projects Agency Wasp micro-air vehicle.