Nonlinear modelling of hysteretic material laws by dual kriging and application Original Research Article

Shape Memory Alloys (SMA) exhibit remarkable mechanical properties, which permit to contemplate a large number of potential applications as actuators, connectors as well as passive or active damping devices. Although a large body of existing patents is available on SMA materials, only a limited number of industrial applications have been implemented up to now. This is probably due to a series of factors, including the absence of recognized mechanical standards, the relatively high cost of raw material, the high temperature dependence of SMA mechanical properties, the sensitivity to heat treatments and finally, the difficulty to model correctly hysteretic material laws. All this is about to change, thanks to recent research advances in modelling and to the appearance of new and less expensive alloy families. The purpose of this paper is to describe the computer aided design tools developed at École Polytechnique de Montréal to model the mechanical behavior of shape memory materials and to calculate the mechanical response of shape memory devices. A new kind of material law for hysteretic materials can be generated by combining a new phenomenological model based on dual kriging with a micromechanical model. The interface between the material law and finite elements can be improved by using, instead of a Von Mises transformation criterion, a Prager type criterion that is well suited for shape memory alloys. Finally, two examples of industrial applications, a Belleville washer for electrical contacts and a medical stent for non-invasive surgery, demonstrate the usefulness of this approach in the design and optimization of shape memory devices.