The Multi-Dimentional Constitutive Relations Of Shape Memory Alloys

Shape memory alloys are materials capable of changing their crystallographic structures due to changes of temperature and/or stress. They exhibit some macroscopic phenomena not present in traditional materials such as shape memory effect, hysteresis, pseudoelasticity and alterable damping capacity. These unique properties have been the focus of many research efforts in the past few years and have given rise to their usage in smart structures as sensors and actuators. As consequence, the design of shape memory alloy devices calls upon accurate and reliable constitutive models to describe the material behavior when immersed in different environment. In this paper, a multi-dimensional constitutive model of shape memory alloys is developed, and the attempts that have been done are as follows:First of all, the characteristics of shape memory alloys as well as their behavior of smaller subunits during transformation are discussed in this paper. Secondly, the constitutive models which have strong influence are classified and summarized on the basis of their mechanics characteristics and fundamentals. The two different methodologies in modeling the three-dimensional constitutive relations are also briefly introduced. In the unified thermodynamic framework presented by Lagoudas et al., the transformation function and the internal state variables are discussed. Basis on the thermodynamic framework, the yield criterion of plasticity and the relation of martensitic fraction, stress and temperature proposed by Liang and Brinson, a multi-dimensional constitutive model is ultimately developed.The constitutive model is programmed and implemented by numerical method. Examples show that the present constitutive model is in agreement with the experimental results, it can simulate the shape memory effect and pesudoelasticity. This new model can also overcome the defect of Lagoudas model, which cannotreflect the action of martensite reorientation when SMA is loaded below the martensitic start temperature. It is suitable for further application in the available nonlinear finite element program and can be realized easily.