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Computational Mechanics
Published in: Computational Mechanics 3/2014

01-09-2014 | Original Paper

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

Authors: A. Javili, A. McBride, P. Steinmann, B. D. Reddy

Published in: Computational Mechanics | Issue 3/2014

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Abstract

A curvilinear-coordinate-based finite element methodology is presented as a basis for a straightforward computational implementation of the theory of surface elasticity that mimics the underlying mathematical and geometrical concepts. An efficient formulation is obtained by adopting the same methodology for both the bulk and the surface. The key steps to evaluate the hyperelastic constitutive relations at the level of the quadrature point in a finite element scheme using this unified approach are provided. The methodology is illustrated through selected numerical examples.
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Footnotes
2
Note that we distinguish between the material, spatial and natural configurations. A line element \(\text{ d }{\varvec{X}}\) in the material configuration is mapped to \(\text{ d }{\varvec{x}}\) in the spatial configuration via the linear map \({\varvec{F}}\) and to \(\text{ d }\varvec{\xi }\) in the natural (reference) configuration via \(\varvec{K}\), see Table 3. The material, spatial and natural configurations on the surface are defined in a near-identical fashion to the bulk, see Table 4.
 
3
The routine used, rsgene2D, produces a Gaussian height distribution with an exponential auto-covariance. The input parameters were 100 divisions, a surface length of 2, a root mean square height of 0.05, and an (isotropic) correlation length of \(0.25\).
 
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Metadata
Title
A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology
Authors
A. Javili
A. McBride
P. Steinmann
B. D. Reddy
Publication date
01-09-2014
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 3/2014
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-014-1030-4

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