One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials

Abstract

The use of the thermoelastic martensitic transformation and its reverse transformation has recently been proposed and demonstrated for several active control ap plications. However, the present constitutive models have lacked several important funda mental concepts that are essential for many of the proposed intelligent material system ap plications such as shape memory hybrid composites. A complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in this paper. The thermomechanical model formulation herein will investigate important material characteristics involved with the internal phase transformation of shape memory alloys. These characteristics include energy dissipation in the material that governs the damping behavior, stress-strain-temperature relations for pseudoelasticity, and the shape memory effect. Some numerical examples using the model are also presented.

Spherical indentation hardness of shape memory alloys

“…Therefore, the transformation volume strain is neglected in our analysis. mathematical models can be found in literatures [15][16][17][18]. To avoid the complexity of tracking the detailed evolution of the material microstructure during the phase transformations, a phenomenological model is adopted in the present investigation [19,20].…”

A shape memory alloy adaptive tuned vibration absorber: design and implementation

“…Here σ is the Piola-Kirchoff stress tensor and ε is the Green strain tensor [10,16,18] because SMA components are usually involved in large strain applications (strains of the order fo 10 -1 rather than 10 -6 ).…”

Theoretical modelling of the effect of plasticity on reverse transformation in superelastic shape memory alloys

“…Many constitutive models for transformation in shape memory alloys have been published [2,9]. Transformation thermomechanical theory, crystallographic theory of martensitic transformation and/or micromechanics approach have been applied to develop some of these models [10][11][12][13]. For the purpose of our present research, a phenomenological model developed by Auricchio et al [14] and Lubliner and Auricchio [15] was modified to describe forward and reverse transformation in superelastic shape memory alloys.…”