NONLINEAR FINITE-ELEMENT SIMULATION OF SUPERELASTIC SHAPE-MEMORY ALLOY PARTS

This article presents a methodology to simulate the nonlinear thermome chanical behaviour of shape memory alloys (SMA) by the finite element method. After a brief presentation of the remarkable thermomechanical properties of SMA materials, a general and simplified constitutive law is formulated based on plastic flow theory, which takes into account the stress and temperature induced phase transformation in the alloy. The reason for this connection between plasticity and the superelastic behaviour of SMA lies in the phase transformation itself the effect o f which is somehow similar to a plastic flow. This approach, however, differs from plasticity in the sense that upon unloading the initial s tate of the material can be recovered through a hysteresis cycle. To s imulate this hysteresis, two different von Mises plastic criteria for three-dimensional problems are used for the loading and unloading proc edures, respectively, so that unloading can also be treated as a trans ition from elasticity to plasticity. It is first suggested to use a bi linear model as uniaxial material law. Then a more precise model based on dual kriging interpolation is also proposed and implemented. The n onlinear finite element equations of the approximate problem are brief ly stated and the methodology is validated by comparison with experime ntal results. Finally, one example of industrial application is given concerning stress analysis of a SMA spring disc. Copyright (C) 1996 El sevier Science Ltd.