Finite elements for elasticity with microstructure and gradient elasticity
Finite elements for elasticity with microstructure and gradient elasticity
We present a general finite element discretisation of Mindlin’s Elasticity with Microstructure. A total of twelve isoparametric elements are developed and presented, six for plane strain conditions and six for the general case of three-dimensional deformation. All elements interpolate both the displacement and microdeformation fields. The minimum order of integration is determined for each element, and they are all shown to pass the single-element test and the patch test. Numerical results for the benchmark problem of one-dimensional deformation show good convergence to the closed-form solution. The
behaviour of all elements is also examined at the limiting case of vanishing relative deformation, where Elasticity with Microstructure degenerates to Gradient Elasticity. An appropriate parameter selection that enforces this degeneration in an approximate manner is presented, and numerical results are shown to provide good approximation to the respective displacements and strains of a gradient elastic solid.
gradient elasticity, elasticity with microstructure, couple stress, higher-order continuum, finite elements, penalty method
564-595
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
22 January 2008
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Zervos, A.
(2008)
Finite elements for elasticity with microstructure and gradient elasticity.
International Journal for Numerical Methods in Engineering, 73 (4), .
(doi:10.1002/nme.2093).
Abstract
We present a general finite element discretisation of Mindlin’s Elasticity with Microstructure. A total of twelve isoparametric elements are developed and presented, six for plane strain conditions and six for the general case of three-dimensional deformation. All elements interpolate both the displacement and microdeformation fields. The minimum order of integration is determined for each element, and they are all shown to pass the single-element test and the patch test. Numerical results for the benchmark problem of one-dimensional deformation show good convergence to the closed-form solution. The
behaviour of all elements is also examined at the limiting case of vanishing relative deformation, where Elasticity with Microstructure degenerates to Gradient Elasticity. An appropriate parameter selection that enforces this degeneration in an approximate manner is presented, and numerical results are shown to provide good approximation to the respective displacements and strains of a gradient elastic solid.
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e-pub ahead of print date: 29 May 2007
Published date: 22 January 2008
Keywords:
gradient elasticity, elasticity with microstructure, couple stress, higher-order continuum, finite elements, penalty method
Identifiers
Local EPrints ID: 53384
URI: http://eprints.soton.ac.uk/id/eprint/53384
ISSN: 0029-5981
PURE UUID: 4ce5f779-a3d6-473d-a45c-67dbaf26766e
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Date deposited: 22 Jul 2008
Last modified: 16 Mar 2024 03:32
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