Data-driven Techniques to Estimate Parameters in the Homogenized Energy Model for Shape Memory Alloys
NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF MATHEMATICS
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The homogenized energy model HEM is a uni ed framework for modeling hysteresis in ferroelectric ferromagnetic, and ferroelastic materials. The HEM framework combines energy analysis at the lattice level with stochastic homogenization techniques, based on the assumption that quantities such as inter- action and coercive fields are manifestations of underlying densities, to construct macroscopic material models. In this paper, we focus on the homogenized energy model for shape memory alloys SMA. Specifically, we develop techniques for estimating model parameters based on attributes of measured data. Both the local mesoscopic and macroscopic models are described, and the model parameters relationship to the materials response are discussed. Using these relationships, techniques for estimating model parameters are presented. The techniques are applied to constant-temperature stress-strain and resistance-strain data. These estimates are used in two manners. In one method, the estimates are considered fixed and only the HEM density functions are optimized. For SMA, the HEM incorporates densities for the interaction and relative stress, the width of the hysteresis loop. In the second method the estimates are included in the optimization algorithm. Both cases are compared to experimental data at various temperatures, and the optimized model parameters are compared to the initial estimates.
- Properties of Metals and Alloys