Development and validation of thermo-mechanically coupled finite elements for the simulation of the nonlinear time response of multi-layered shape memory alloy beams
The scope of the present work is the development of numerically efficient finite elements for the simulation of the transient, thermo-mechanically coupled and non-linear behavior of shape memory alloys (SMA)s. Therefore, the work focuses in two scientific fields: 1) the development of an improved constitutive model describing the SMA behavior and 2) the development of nonlinear thermo-mechanically coupled beam FEs implementing the developed SMA constitutive model. In the first part of the dissertation a new SMA constitutive model is presented which is developed based on the widely recognized constitutive model of Lagoudas et al. (2012). New terms are introduced in the model that enhance its accuracy and eliminate numerical issues encountered by the usage of the baseline model in the FE analysis framework. Furthermore, the model is implemented in the continuum elements of ABAQUS commercial software through a user material subroutine (UMAT). In the second part of the dissertation, beam FEs are developed that incorporate the developed SMA constitutive model and provide significant computational advantages compared to the continuum FEs. The new FEs implement the thermo-mechanically coupled equilibrium equations in conjunction with properly chosen thermo-mechanical field kinematic assumptions for the simulation of the transient response of beam structures which admit various layers of SMA and passive materials. Initially the formulation of a geometrically linear beam FE is presented while subsequently a second formulation is presented, suitable for the simulation of structures which admits large displacements and rotations by capturing their geometrically nonlinear response. The equilibrium equations of both FE formulations are presented and implemented in the nonlinear FE framework of ABAQUS through the UEL subroutine. Therefore, the equations are solved using the Newton-Raphson nonlinear iterative solution technique while the necessary time integrations are performed numerically by the adoption of the implicit time integration scheme. The comparison of the numerical results acquired through the beam FE and the continuum FE models, implementing the same SMA constitutive model, demonstrates the perfect agreement and proves the efficiency of the chosen multi-field kinematic assumptions regarding the beam model while at the same time highlights the superiority of the beam FE model in terms of computational speed. Finally, the correlation between the actual experimentally measured and the respective predicted response of morphing structures validates the results of both the developed beam FE and the SMA constitutive model.
Finite elements, Shape memory alloys, 669.95, Πεπερασμένα στοιχεία, Κράματα μνήμης σχήματος
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