On volumetric locking-free behaviour of p-version finite elements under finite deformations

Ulrich Heisserer; Stefan Hartmann; Alexander Düster; Zohar Yosibash

doi:10.1002/cnm.1008

On volumetric locking-free behaviour of p-version finite elements under finite deformations

Ulrich Heisserer^*, Stefan Hartmann, Alexander Düster, Zohar Yosibash

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.

Original language	English
Pages (from-to)	1019-1032
Number of pages	14
Journal	Communications in Numerical Methods in Engineering
Volume	24
Issue number	11
DOIs	https://doi.org/10.1002/cnm.1008
State	Published - Nov 2008
Externally published	Yes

Keywords

Axisymmetry
Finite strains
Hyper-elasticity
Locking-free
Nearly incompressible Neo-Hooke material
p-FEM

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10.1002/cnm.1008

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title = "On volumetric locking-free behaviour of p-version finite elements under finite deformations",

abstract = "We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.",

keywords = "Axisymmetry, Finite strains, Hyper-elasticity, Locking-free, Nearly incompressible Neo-Hooke material, p-FEM",

author = "Ulrich Heisserer and Stefan Hartmann and Alexander D{\"u}ster and Zohar Yosibash",

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AU - Hartmann, Stefan

AU - Düster, Alexander

AU - Yosibash, Zohar

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Y1 - 2008/11

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AB - We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.

KW - Axisymmetry

KW - Finite strains

KW - Hyper-elasticity

KW - Locking-free

KW - Nearly incompressible Neo-Hooke material

KW - p-FEM

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ER -

On volumetric locking-free behaviour of p-version finite elements under finite deformations

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Keywords

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