CUED Publications database

An unstructured immersed finite element method for nonlinear solid mechanics

Rüberg, T and Cirak, F and García Aznar, JM (2016) An unstructured immersed finite element method for nonlinear solid mechanics. Advanced Modeling and Simulation in Engineering Sciences, 3.

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Abstract

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:55
Last Modified: 17 Oct 2017 01:38
DOI: