Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
Finite element approach to modelling evolution of 3D shape memory materials
Mathematics and Computers in Simulation
Coupling control and human factors in mathematical models of complex systems
Engineering Applications of Artificial Intelligence
Numerical simulation of phase transformations in shape memory alloy thin films
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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Despite recent progress in modelling the shape memory alloy (SMA) behaviour, many difficulties remain due to various limitations of the existing free energy models and strong nonlinearity of these nonlinear materials. Phase kinetics of SMA coupled with thermoelastodynamics is still not fully tractable, and one needs to deal with complicated multiscale character of SMA materials requiring a linkage between their microstructure and macroscopic properties. In this paper we develop a new dynamic model of 3D SMA which employs an improved version of the microscopic Landau theory. Essential properties of the single and multivariant martensitic phase transformations are recovered using consistent steps, which eliminates the problem of non-uniqueness of energy partitioning and relaxes the over-sensitivity of the free energy due to many unknown material constants in previously reported models. We exemplify our results on a model for cubic to tetragonal transformations in a rectangular SMA bar by showing key algorithmic steps which can be extended to more complex cases.