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Analytical and Numerical Investigations of Locking in Transversely Isotropic Elasticity
09 Nov
09. November 2018
Vortrag

Analytical and Numerical Investigations of Locking in Transversely Isotropic Elasticity

For isotropic materials the concept of volumetric locking in the context of low-order finite element approximations is well understood, and a variety of effective remedies exist: for example, the use of mixed methods, discontinuous Galerkin (DG) methods, or selective underintegration. Corresponding studies have been carried out, to a limited extent, to determine conditions under which locking related to inextensibility occurs, in small- and large-deformation contexts. The models treated in these works are of an isotropic material, with inextensibility imposed as a constraint. The present work is concerned with transversely isotropic linear elastic materials, which are characterized by 5 material parameters. The behaviour under limiting conditions of near-incompressibility and near-inextensibility are investigated. It is shown both through numerical examples and an analysis of finite element approximations that locking behaviour for low-order elements depends critically on the degree of anisotropy of the material, in particular on the ratio of Young’s moduli for the directions parallel and transverse to the direction characterizing transverse isotropy. Various low-order finite element approximations are pursued: first, conforming approximations are considered, and it is shown that selective reduced integration is necessary for uniform convergence. The second approach concerns DG approximations, where selective under-integration of edge terms is required for convergence in the inextensible limit. The final approximation uses the Virtual Element Method (VEM), which is shown to be robust in the inextensible and incompressible limits. For VEM approximations, both homogeneous and non-homogeneous bodies (respectively constant and variable fibre direction) are treated.

Speaker

Prof. Daya Reddy
Centre for Research in Computational and Applied Mechanics
University of Cape Town, South Africa

Organiser

Graduate School MUSiC with the IRTG 1627

Date

09. November 2018
10:00 o'clock - 11:30 o'clock

Public contact

Dorit Schulte
Institute of Continuum Mechanics
Appelstr 11
30167 Hannover
Tel.: +49 511 762 17834
schulte@ikm.uni-hannover.de

Location

Institut für Kontinuumsmechanik
Building: 3404
Room: A 501
MUSiC Seminar Room
Appelstraße 11
30167 Hannover
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