Mesoscopic free energy as a framework for modeling shape memory alloys

Abstract

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.

Hybrid Dynamical Modeling of Polycrystalline Shape Memory Alloy Wire Transducers

“…A valuable baseline is offered by the mesoscopic MAS model for polycrystalline SMA material presented by Rizzello et al (2019). Such a model is based on a novel bookkeping algorithm that reproduces the time evolution of smooth hysteresis loops, as well as inner loops, while maintaining all physical information of the basic single-crystal MAS model (Ballew and Seelecke (2019)). Despite those advantages, the model is affected by slow simulation time due to strong nonlinearities and numerical stiffness of the resulting ODEs.…”

“…When SMA material is heated, transformations in the crystal lattice structure are induced, which generate a macroscopic change in shape on the order of 4-8%. This effect can be exploited for the development of novel actuators that react to an external thermal input with a mechanical deformation (Ballew and Seelecke (2019)). In most applications, SMA material is shaped as a thin wire.…”

A Hybrid Dynamical Modeling Framework for Shape Memory Alloy Wire Actuated Structures

“…where ω x is a natural frequency associated to thermal activation, V L is the volume of a mesoscopic crystal layer, k B is the Boltzmann constant, T is the SMA temperature, and ∆g αβ (σ, T ) is the Gibbs free-energy barrier of the phase transformation. The energy barriers ∆g αβ depend in a complex mathematical way on the transformation stresses of austenite and martensite, denoted as σ A and σ M respectively (details are omitted for conciseness, the reader may refer to [12], [13] for details). Such quantities are given by…”

“…With the aim of developing improved numerical tools for SMA systems, in this paper we present a novel hybrid model for single-crystal SMA wire actuators. The proposed hybrid reformulation is grounded on the SMA model originally developed by Müller-Achenbach-Seelecke (MAS) which, in turn, is based on a statistical thermodynamic framework [12], [13]. Due to its physics-based nature, the MAS model allows to effectively describe the hysteretic behavior of SMA wire actuators under different operating conditions and thermomechanical loads.…”

Modeling and Position Control Simulation Research on Shape Memory Alloy Spring Actuator

“…S. Seelecke and I. Muller gave an overview of shape memory alloy applications in the field of smart structure actuation [6] and S. Seelecke reinterpreted the one-dimensional SMA model. The model is based on a continuous, multi-well free energy that governs the phase change at a mesoscopic material scale, and the model offers extended capabilities and a simpler formulation [7]. Coiled SMA actuators can be used to drive a 3D-printing manipulator [8].…”