Past Event: Oden Institute Seminar

Dissertation Work

Nabil Abboud, Ph.D. candidate, Department of Civil and Environmental Engineering (CEE), Duke University

Abstract

The main goal of my PhD work is to develop a robust, efficient, accurate, and stable finite element based framework to simulate small and large deformation solid mechanics’ problems involving complex geometries and complicated incompressible constitutive models. A third aspect, of practical importance, that is considered in my work is time-dependency. At the base of the aforementioned framework is the use of tetrahedral finite elements, with linear shape functions, and the variational multiscale approach. The stability of the proposed algorithm was evaluated using an extensive set of numerical tests from the literature, as well as a thorough numerical analysis in the particular case of quasi-static J2-elasto-plasticity. From this extensive set of numerical tests, it was shown that the algorithm is invariant to the constitutive model and the time integrator used. Through a series of convergence tests, the algorithm was shown to have optimal rates of convergence, in the L2 norm, for the displacements, and velocities, and sub-optimal rate of convergence for the pressure. Finally, the robustness of the algorithm is showcased by considering realistic test cases involving complicated geometries and very large deformation. BIO Nabil Abboud is a Ph.D. candidate in the Department of Civil and Environmental Engineering (CEE) at Duke University. His research interests are Finite element, numerical analysis, fluid-structure interaction, computational solid mechanics, and computational fluid mechanics. His thesis, “Stabilized finite elements for problems involving complex constitutive models and irregular geometries” is in progress. He is advised by Professor Guglielmo Scovazzi.