Vol. 3, No. 8, 2008

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A generalized Cosserat point element (CPE) for isotropic nonlinear elastic materials including irregular 3-D brick and thin structures

M. Jabareen and M. B. Rubin

Vol. 3 (2008), No. 8, 1465–1498

A generalized form for the strain energy of inhomogeneous deformations is developed for a 3-D brick Cosserat Point Element (CPE) which includes full coupling of bending and torsional modes of deformation. The constitutive coefficients, which depend on the reference geometry of the element, are determined by solving eighteen bending problems and six torsion problems on special elements that are parallelepipeds with two right angles. The resulting constitutive coefficients ensure that the strain energy for inhomogeneous deformations remains a positive definite function of the inhomogeneous strain measures for all reference element shapes. A number of example problems are considered which show that the generalized CPE produces results as accurate as enhanced strain and incompatible elements for thin structures and is free of hourglass instabilities typically predicted by these enhanced elements in regions experiencing combined high compression with bending.

Cosserat point, element irregularity, finite element, nonlinear elasticity
Received: 22 December 2007
Revised: 26 June 2008
Accepted: 29 June 2008
Published: 1 October 2008
M. Jabareen
Institute of Mechanical Systems
Department of Mechanical Engineering
ETH Zentrum
8092 Zürich
M. B. Rubin
Faculty of Mechanical Engineering
Technion – Israel Institute of Technology
32000 Haifa