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Sergi Pérez-Escudero obtained the Bachelor’s degree in Mathematics at the Universitat de València in 2020 and the Master’s degree in Advanced Mathematics and Mathematical Engineering at UPC in 2021. Since January 2022, he is a PhD candidate in the research group of electroactive materials in LaCàN (UPC), under the supervision of Profs. Sonia Fernández-Méndez and Irene Arias. Funded by the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR), his work focuses on the development of FE schemes for the numerical solution of the flexoelectric and the flexo-photovoltaic effect, and their implementation in an in-house MATLAB code.
This PhD thesis focuses in the numerical modeling of flexoelectricity and flexo-photovoltaics, both at infinitesimal and finite deformations, using standard C0 Finite Element (FE) approximations.
On one side, an alternative formulation to the drift-diffusion semiconductor modeling equations, relying on adimensionalized logarithmic quantities, is developed. The FE implementation of both formulations in an in-house MATLAB code is able to reproduce benchmark problems, demonstrating the benefit of the logarithmic formulation in convection-dominated scenarios, where coarser meshes are able to provide solutions without spurious oscillations. Furthermore, two nonlinear solvers are assessed and compared: a monolithic Newton-Raphson method and the Gummel method.
On the other side, the focus is placed on the development of the extension of C0 Interior Penalty formulations for the solution of the partial differential equations (PDE) modeling linear flexoelectricity, including additional gradient dielectricity and converse flexoelectricity effects, and on the development of a combined C0 Interior Penalty Newton-Raphson method for the solution of the nonlinear PDE modeling flexoelectricity at finite strains. The proposed schemes are able to avoid the drawbacks of C1 approximation spaces or mixed formulations, enabling the solution of 4th-order PDE by standard FE approximations. The computational implementation of the developed numerical schemes has shown the expected high-order convergence of the methods, and is able to reproduce benchmark problems. Moreover, the developed frameworks are extended, incorporating generalized periodicity boundary conditions, to reproduce apparent piezoelectric metamaterials at large deformations.
Finally, the coupling of flexoelectricity and semiconductor modeling is carried out. Proof of concept experiments, simulated with the FE solution of the proposed coupled continuum model at infinitesimal deformations, are reported, comparing the obtained results with standard photovoltaic simulations. In addition, the thesis provides a continuum modeling approach for the flexo-photovoltaic effect at finite deformations.
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