The homogenized energy model (HEM) is a unified 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 interaction 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 material's 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.

A novel hybrid process for drawing operations is proposed. This process combines the conventional drawing and hydroforming features. The hybrid drawing die assembly is designed to incorporate multiple die segments engraved with high pressure fluid channels. Preliminary results on drawn Al 6061 specimens under two fluid pressure levels showed that the drawing load can decrease significantly. The hybrid drawing process has also shown that varying the fluid pressure can alter the surface asperities at the tool-workpiece interface in real-time, promoting micro-pool lubrication. This was evidenced by distinct surface topographies observed via scanning electron micrographs and optical micrographs.