The paper presents a numerical implementation of the ZM model for shape memory alloys that fully accounts for non-proportional loading and its influence on martensite reorientation and phase transformation. Derivation of the time-discrete implicit integration algorithm is provided. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. The simulations are shown to agree with experimental and numerical simulation data taken from the literature.
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Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases
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Zaki, W, Gu, X, Morin, C, Moumni, Z, & Zhang, W. "Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases." Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation and Control of Adaptive Systems; Structural Health Monitoring; Keynote Presentation. Newport, Rhode Island, USA. September 8–10, 2014. V001T03A024. ASME. https://doi.org/10.1115/SMASIS2014-7599
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