Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

Abstract

The homogenized energy model is a unified framework for modeling hysteresis in ferroelectric, ferromagnetic, and ferroelastic materials. The homogenized energy model framework combines energy analysis at the lattice level with stochastic homogenization techniques, based on the assumption that quantities such as interaction and coercive fields are manifestations of underlying densities, to construct macroscopic material models. In this article, we focus on the homogenized energy model for shape memory alloys. 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 material’s response is 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 homogenized energy model 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.