One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable

Abstract

A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable ap proach is used to derive a comprehensive constitutive law for shape memory alloy materials from first principles without the assumption of constant material functions. This constitutive law is of such a form that it is well suited to further practical engineering applications and calculations. A separation of the martensite fraction internal variable into temperature-induced and stress- induced parts is presented and justified, which then allows the derived constitutive law to accurately represent both the pseudoelastic and shape memory effects at all temperatures. Several numerical ex amples are given that illustrate the ability of the constitutive law to capture the unique thermome chanical behavior of shape memory alloys due to their internal phase transformations with stress and temperature.

In-situ studies on martensitic transformation and high-temperature shape memory in small volume zirconia

“…However, the transformation stresses (~1e2.5 GPa) are much higher than for alloys [2], resulting in much higher energies, including actuation energy and damping capacity. Since the martensitic transformation temperature in zirconia is highly tunable through material composition [35] up to 1100 C, it seems worthwhile to explore shape memory properties of zirconia under a variety of extreme conditions.…”

Free Vibration of Thermally Pre/Post-Buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

“…Using one-dimensional constitutive equations for SMA, the recovery stress of SMA fibers is given by the following relation [21,25]:…”

“…For T > A s and C A T − A f < s < C A T − A s , s and T are computed from the following relations [25]:…”

“…We use the one-dimensional constitutive relation proposed by Brinson [25] to find the recovery stress in the SMA fiber. The plate edge is either simply supported with boundary points restrained from moving in the radial direction or clamped.…”

Dynamics of SMA micro-actuator in biomechanical system

“…The microscopic models treat phenomena on a molecular level, therefore the macroscopic phenomenological models are more attractive from practical point of view. In the literature one can find a lot of interesting and thorough description of SMAs [4][5][6][7][8][9][10] and their applications [11][12][13][14]. Different models of SMA give various results depending on nonlinear phenomenon which are taken into account.…”