Modeling of SMA superelastic behavior with nonlocal approach

AbstractDue to their thermomechanical properties (high mechanical work/volume ratio), shape memory alloys (SMA) are particularly interesting to be adopted in the design of micro-sensors and micro-actuators. Thus, various constitutive models have been developed and implemented in finite element codes in order to design such applications. If these ‘local’ models are well adapted to describe the behavior of the bulk material, they fail to satisfactorily describe phenomena such as transformation localization or size effects observed in small samples.A gradient constitutive model is presented in order to describe the localization of phase transformation in SMA structures. To achieve this development restricted to superelasticity, a non local variable (martensite volume fraction) is defined at a material point as the weighted average over the entire material domain of the local transformation variable. Using Taylor expansions, the non local definition is substituted by a gradient based equation, introducing a material length parameter which controls the size of the localization zone.The gradient and mechanical equilibrium constitutive equations have been numerically integrated by using the finite element method. Two kinds of finite elements have been developed (1D truss and 2D quadrilateral) and implemented in Abaqus®via a UEL subroutine. Several simulations have been performed which exhibit the localization phenomena of phase transformation in structures undergoing mechanical loading