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

Abstract

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.

Modeling and Bayesian Parameter Estimation for Shape Memory Alloy Bending Actuators

“…where p(ŷ | q ) is the likelihood of observingŷ given parameters q. For relatively few parameters, the posterior density can be calculated directly by integrating the denominator in Equation (17). However, in higher-dimension parameter spaces, this approach is infeasible.…”

“…The density coefficients α k,m and β k and parameters c k , µ Rm , and b k can be estimated using experimental data. 17 The mesoscopic (or local) strain ε(σ(t) + σ I , T (t); σ R ) in Equation 4is given by…”

“…The transition rates p αβ (α, β = A, M +, M −) depend on the SMA stress, temperature, and material parameters and are described in greater detail in Crews et al 17 The temperature in the SMA actuator is quantified using a first-order, lumped capacitance model,Ṫ…”

“…The homogenized energy model (HEM) is used, which has been applied to various smart materials. [11][12][13][14][15][16][17][18][19][20] The approach to quantify uncertainty is described, including optimization of model parameters and the Markov Chain Monte Carlo method used here. Finally, the results are presented.…”

Multi-Objective Design Optimization of a Shape Memory Alloy Flexural Actuator

“…With this configuration, the microcatheter's release point within the cross section of the CHA could be precisely regulated while keeping the catheter parallel with the surrounding blood flow. In this paper, we build on our previous research [9] to present a design optimization strategy for shape-set flexural actuators based on the homogenized energy framework [10,11]. Previous research on flexural actuators has focused on modeling and understanding the influences of flexible beam composition.…”