A non-local implicit gradient-enhanced model for thermomechanical behavior of shape memory alloys (Co-supervised by Dr. Kadkhodaei)
Year: Sept. 2011- Jan. 2016
Shape memory alloys (SMAs) are a group of smart materials which can recover their shape even after severe deformations. Hence, they are extensively used in various areas such as medical appliances, automotive engineering, robotics, and aerospace. The mechanism of the shape recovery ability is based on the solid-to-solid phase transformation between martensite and austenite phases which can be induced by changes in either temperature or stress. In this thesis, a gradient-enhanced 3-D phenomenological model for shape memory alloys using the non-local theory is developed based on a 1-D constitutive model. The method utilizes a non-local field variable in its constitutive framework with an implicit gradient formulation in order to achieve results independent of the finite element discretization. An efficient numerical approach to implement the non-local gradient-enhanced model in finite element codes is proposed. Based on the implicit radial return scheme, a robust integration scheme is proposed using which the model is implemented in ABAQUS commercial finite element code through a user element subroutine (UEL). The model is used to simulate stress drop at the onset of transformation, and its performance is evaluated using different experimental data. The potential of the presented numerical approach for behavior of shape memory alloys in eliminating mesh-dependent simulations is validated by conducting various localization problems. The numerical results show that the developed model can simulate the observed unstable behaviors such as stress drop and deviation of local strain from global strain during nucleation and propagation of martensitic phase. Moreover, the conducted finite element simulations represent that the inherent mesh sensitivity of the numerical simulation in the presence of softening phenomenon can be removed. This is a significant advantage while using the gradientdependent model. Finally, various material instabilities of SMAs such as softening and divergence of local–global strain are simulated using the proposed non-local model. Also, influence of loading history on the start of the phase transformation during both forward and reverse transformations is considered in the model by introducing new transformation limits and phase fraction formulations. The phase transformation in SMAs is accompanied by a release/absorption of latent heat, which can influence the temperature of the material. This dependency is due to temperature effects rather than strain rates effects. In order to develop more efficient SMAs constitutive model, considering both unstable behavior and thermo-mechanical coupling effects is necessary. Hence, the temperature effect is also simulated by extending the model to include the thermomechanical coupling of the material with its environment. Finally, based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, the proposed small strain model is extended to finite deformation.
Keywords: Shape memory alloys, Non-local model, Unstable behaviors, Finite element, Thermo-mechanical coupling