A Thermomechanical Model for a One Variant Shape Memory Material

Abstract

A model is examined for thermoelastic materials, such as those that display the shape memory and pseudoelastic effect. As is common with models for these materials, an internal variable is utilized which gives the phase fraction of austenite at the microstructural level within the continua. Evolution equations are developed that govern the time history of the system based on changes in stress, strain and temperature. Hysteresis is inherent in the system due to the Duhem- Madelung form of one of these equations. Attention is focused on the connection between complete transformation phenomena and arrested loading/unloading (outer loops vs. subloops); the transition from isothermal to adiabatic loading via loading in a heat convective environment; the identification of attracting states associated with both temperature cycling and periodic stressing; and the deter mination of mathematical restrictions on otherwise rather general constitutive entities entering the model so as to ensure well-posedness, proper qualitative behavior and admissible thermodynamic behavior.

Numerical Simulation of a Semi-Active Vibration Control Device Based on Superelastic Shape Memory Alloy Wires

“…The model must be able to conveniently cope with the relevant set of SMA's properties regarding the type of application at stake. While strain or stress rate independent models McCormick et al, 2006), may be well suited for quasi-static analysis when isothermal conditions may be assumed, for most dynamic applications, rate dependent models are usually required, due to self-heating (Ivshin & Pence, 1994;Liang & Rogers, 1990;Tanaka et al, 1986).…”

“…The Ivshin-Pence mechanical law (Ivshin & Pence, 1994) can be recovered by adding the thermal strain component to the above equation, to read,…”

“…Several kinetic laws are available in the literature, ranging from linear (Auricchio & Sacco, 1997) or exponential laws (Tanaka et al, 1986), to cosine based kinetic laws (Liang & Rogers, 1990) and thermodynamically derived relations (Ivshin & Pence, 1994).…”

Constitutive Model of Shape Memory Alloy considering the effect of Martensite Plasticity for Biomedical Applications

“…However, there are very few constitutive models considering the plastic deformation of the martensite under the conditions of stress-induced martensite transformation. Recently, Kan and Yan [5][6] developed a temperature-dependent three-dimensional phenomenological constitutive model considering the local plastic yield of martensite under high stress, and then successfully implemented into a finite element package ABAQUS.…”

Mechanics of Shape Memory Alloy Materials – Constitutive Modeling and Numerical Implications

“…As is shown in these studies the thermomechanical response of SMAs is extremely complex, a fact that in conjunction with the continuously increasing use of SMAs in several innovating applications in many engineering fields results in a greater need for a better understanding of these materials. For the past decades several constitutive models have appeared within the literature (e.g., Raniecki et al, 1992;Abeyaratne and Knowles, 1993;Ivshin and Pence, 1994;Boyd and Lagoudas, 1996;Lubliner and Auricchio, 1996;Panoskaltsis et al, 2004), which within the context of a geometrical linear theory can capture several aspects of the experimentally observed response. Nevertheless, the physics of the problem (e.g., see Smallman and Bishop, 2000), together with some basic results of the crystallographic theory of martensitic phase transformations (e.g., Ball and James, 1987;James and Hane, 2000;Abeyaratne et al 2001), suggest that a geometrically non -linear approach is more appropriate.…”