Enriched finite element methods for the analysis of complex microstructures

Dongyu Liu (PhD candidate) and Alejandro M. Aragón (supervisor)

This project is on different applications of enriched finite element methods to the characterization of polycrystalline microstructures, contact analysis, and the modeling of fiber reinforced composites. Such problems are quite common and important in engineering, yet they are usually hard to be modeled with the standard finite element method efficiently or accurately. The interface-enriched generalized finite element method (IGFEM) and the discontinuity-enriched finite element method (DE-FEM) are both used in this project to decouple the finite element discretization from the geometric features of the problem. Some extensions of these methods, such as developing new enrichment functions and combining and implementing reduced order models are being investigated to increase the versatility of these methods in pursuit of solving the aforementioned problems more efficiently and accurately.

Stress field of a star shaped branched crack
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