Transformation and Plasticity of Shape Memory Alloy Structures: Constitutive Modeling and Finite Element Implementation
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Transformation and Plasticity of Shape Memory Alloy Structures: Constitutive Modeling and Finite Element Implementation Mohammad Javad Ashrafi (Submitted April 24, 2020; in revised form June 25, 2020) In this work, we extend a well-known three-dimensional phenomenological shape memory alloy (SMA) constitutive model known as Souza model. The proposed model describes more precisely the hardening behavior observed during forward- and reverse-phase transformation as well as evolution of plastic strain and its effects on transformation behavior. Moreover, we present a solution algorithm for low temperatures and evolution of plastic strains which considerably reduces the computational cost. Through calibration of material parameters, the model is able to predict pseudo-elasticity and shape memory properties of SMAs more accurately compared to Souza model. Moreover, the plasticity and its effect on transformation are well predicted by the proposed model. Through finite element implementation, we can perform simulations on complex SMA structures. Finally we compare the run time for the present algorithm with the iterative Newton method used for solving equations of Souza model. The comparisons show that the computational cost of the proposed algorithm is considerably lower than previous algorithms. Keywords
finite element implementation, phase transformation solution algorithm, plasticity, shape memory alloys
1. Introduction Smart materials attracted the attention of many researches due to their innovative applications in various fields of engineering and medicine. Shape memory alloys (SMAs), as an interesting type of smart materials, have two main features known as pseudo-elasticity and shape memory effect which make them good choices for actuators and smart deformable objects in different industries (Ref 19, 20, 22). In the past decades, many researchers have worked on thermomechanical modeling of SMAs and implemented their models in the analysis of various structures made of SMAs. There are several approaches in the modeling of SMAs such as micromechanical and phenomenological approaches. From the aspect of simple numerical implementation and simulation of various SMA structures with adequate accuracy, phenomenological approaches have been proved to be efficient. In a phenomenological model, appropriate internal variables should be chosen to represent the primary features of SMAs. In general, a tensorial and/or a scalar internal variable are utilized to study phase transformation and plasticity of SMAs under proportional and non-proportional loadings (Ref 3, 15, 21, 27, 28). From the viewpoint of applicability and computational cost, the models which capture more accurately the features of SMAs require more computational cost and calibration of a large number of model parameters (Ref 16, 18, 23, 27). Mohammad Javad Ashrafi, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran. Contact e-mail: mj_ashrafi@iust.ac.ir.
Journal of Materials
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