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Approximate Models of Dynamic Thermoviscoelasticity Describing Shape-Memory-Alloy Phase Transitions

R. V. N. Melnik, A. J. Roberts

TL;DR

This paper develops efficient approximate models for dynamic thermoviscoelasticity with nonlocal coupling and finite speed heat propagation, focusing on shape memory alloys. It integrates nonlocal continuum mechanics, Cattaneo-Vernotte heat conduction, Landau-Devonshire free energy, and centre-manifold reductions to derive 1D hyperbolic models and 3D slow-manifold reductions. Computational experiments illustrate thermally and mechanically induced phase transformations, hysteresis, and memory effects in shape-memory alloys. The framework provides practical tools for predicting complex thermoelastic responses in SMA structures and informs design of memory-material devices.

Abstract

We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy structures are presented.

Approximate Models of Dynamic Thermoviscoelasticity Describing Shape-Memory-Alloy Phase Transitions

TL;DR

This paper develops efficient approximate models for dynamic thermoviscoelasticity with nonlocal coupling and finite speed heat propagation, focusing on shape memory alloys. It integrates nonlocal continuum mechanics, Cattaneo-Vernotte heat conduction, Landau-Devonshire free energy, and centre-manifold reductions to derive 1D hyperbolic models and 3D slow-manifold reductions. Computational experiments illustrate thermally and mechanically induced phase transformations, hysteresis, and memory effects in shape-memory alloys. The framework provides practical tools for predicting complex thermoelastic responses in SMA structures and informs design of memory-material devices.

Abstract

We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy structures are presented.

Paper Structure

This paper contains 9 sections, 50 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Notation
  3. Nonlocal Models of Thermoviscoelasticity
  4. The Cattaneo-Vernotte Model for Heat Conduction
  5. The Landau-Devonshire Model for the Helmholtz Free Energy and the Stress-Strain Relation
  6. One-Dimensional Hyperbolic Approximation of Shape-Memory-Alloy Dynamics
  7. Computational Experiments
  8. Construction of Approximate Models for Dynamic Thermoviscoelasticity Using Centre Manifold Theory
  9. Acknowledgements

Figures (2)

  • Figure 1: Thermally induced phase transformations.
  • Figure 2: Mechanically induced phase transitions.

Theorems & Definitions (2)

  • Remark 5..1
  • Remark 5..2