Abstracts Engineering

A Hierarchical Interface-enriched Finite Element Method forthe Simulation of Problems with Complex Morphologies

by Cruz Jorge Barrera

In the last few decades, the finite element method (FEM) has become one of the most important computational tools for the simulation of engineering problems. Due to the increasing popularity of this method, a heavy body of research has focused its attention to the development of advanced FEM-based techniques for the treatment of complex phenomena, including intricate morphologies. This thesis introduces a hierarchical interface-enriched finite element method (HIFEM) for the mesh-independent treatment of the mentioned type of problems. The HIFEM provides a general, and yet easy-to-implement algorithm for evaluating appropriate enrichment in elements cut by multiple interfaces. In the automated framework provided by this method, the construction of enrichment functions is independent of the number and sequence of the geometries introduced to nonconforming finite element meshes. Consequently, the HIFEM algorithm eliminates the need to modify/remove existing enrichment every time a new geometry is added to the domain. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along material interfaces that are in close proximity, in contact, or intersecting with one another using nonconforming finite element meshes for discretizing the problem. The main contribution of this thesis is the development and implementation of the two-dimensional higher-order HIFEM, and in particular the development of a new hierarchical enrichment scheme for six-note triangular elements. Furthermore, this manuscript presents a new enrichment scheme to simulate strong discontinuities (cracks) in linear elastic fracture mechanics problems. Special attention is given to the available strategies to improve the level of precision and efficiency of the simulations. A detailed convergence study for the enrichment technique that yields the highest precision and the lowest computational cost is also presented. Finally, the author illustrates the application of the higher-order HIFEM for simulating the thermal and deformation responses of a variety of engineering problems with complex geometries, including porous media, fiber-reinforced composites, and quasi- static cracks in a heterogeneous domain. Advisors/Committee Members: Soghrati, Soheil (Advisor).