Computational Modeling

Advancing finite element technology for designing materials and structures

Known about since the mid-twentienth century, the Finite Element Method (FEM) is a numerical procedure used to analyze problems in physics and engineering. FEM works by subdividing a large problem into smaller, simpler parts called finite elements. This discretization process results in a so-called finite element mesh that is subsequently used for the analysis. Although the behavior within each element is simple, once reassembled, they can reproduce very complex behavior.

In order to preserve accuracy, FEM relies on a "matching mesh", where the sides of the elements align with the problem geometry. However, Aragón has worked for years on "Enriched Finite Element Methods (EFEM)" as a way to analyze problems with meshes that are decoupled from the problem’s geometric features. This is possible by means of "enrichment functions", which incorporate a priori knowledge about the solution to the problem, thereby augmenting the standard finite element space by an enriched space that recovers the accuracy otherwise lost by the use of a non-matching discretization.

New enriched finite element technology is being developed at SOM for many problems in continuum mechanics, including the analysis of composite materials (weak discontinuities), fracture (strong discontinuities), immerse boundary (or fictitious domain) problems, contact mechanics, among others.

 

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