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An unstructured immersed finite element method for nonlinear solid mechanics.

Published version
Peer-reviewed

Type

Article

Change log

Authors

Rüberg, Thomas 
García Aznar, José Manuel 

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.

Description

Keywords

CSG modelling, Cut-element stabilisation, Immersed finite elements, Implicit geometry, Nitsche’s method, Nonlinear solid mechanics

Journal Title

Adv Model Simul Eng Sci

Conference Name

Journal ISSN

2213-7467
2213-7467

Volume Title

3

Publisher

Springer Science and Business Media LLC
Sponsorship
Engineering and Physical Sciences Research Council (EP/G008531/1)
This work was partially supported by the EPSRC (second author, Grant #EP/G008531/1), by the European Research Council (third author, Grant #ERC-2012-StG 306751), and by the Spanish Ministry of Economy and Competitiveness (third author, Grant #DPI2015-64221-C2-1-R).