Three Dimensional Modeling and a Simulation of the Shape Memory Effect

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Scientific Technical Review
The paper deals with modeling and simulating the shape memory effect , one of many behaviors of shape memory alloys. The effect was first divided into three stages. Every stage has its own thermodynamic potential and constitutive equations. The martensite fraction is the only internal variable to be considered: in the first stage, it represents the fraction of detwinned martensite; in the second stage, it represents the fraction of transformed martensite into austenite, and in the last stage, it represents the fraction of the produced martensite from the austenite transformation. For every stage, we deduced the constitutive equations using the principles of thermodynamics and a simple formalism. When the model was defined, we simulated it using the experimental data obtained by analyzing a cube specimen subjected to triaxial traction and thermal load. The obtained results of this simulation reflect the behavior of this kind of materials when thermomechanical load is applied. The main finding of this paper is that the proposed constitutive model can be used to simulate the shape memory effect.