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Tetrahedral composite finite elements

Thoutireddy, P. and Molinari, J. F. and Repetto, E. A. and Ortiz, M. (2001) Tetrahedral composite finite elements. International Journal for Numerical Methods in Engineering, 53 (6). pp. 1337-1351. ISSN 0029-5981.

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We develop and analyse a composite ‘CT3D’ tetrahedral element consisting of an ensemble of 12 four-node linear tetrahedral elements, coupled to a linear assumed deformation defined over the entire domain of the composite element. The element is designed to have well-defined lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of volume constraints per element. The relation between displacements and deformations is enforced weakly by recourse to the Hu–Washizu principle. The element arrays are formulated in accordance with the ‘assumed-strain’ prescription. The formulation of the element accounts for fully non-linear kinematics. Integrals over the domain of the element are computed by a five-point quadrature rule. The element passes the patch test in arbitrarily distorted configurations. Our numerical tests demonstrate that CT element has been found to possess a convergence rate comparable to those of linear simplicial elements, and that these convergence rates are maintained as the near-incompressible limit is approached. We have also verified that the element satisfies the Babuška–Brezzi condition for a regular mesh configuration. These tests suggest that the CT3D element can indeed be used reliably in calculations involving near-incompressible behaviour which arises, e.g., in the presence of unconfined plastic flow.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Additional Information:© 2001 John Wiley & Sons. Received 14 August 2000.Revised 9 February 2001. The support of the Department of Energy through Caltech’s ASCI/ASAP Center for the Simulation of the Dynamic Behavior of Materials is gratefully acknowledged.
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:finite element analysis; composite element; contact; dynamics; inf–sup test
Issue or Number:6
Record Number:CaltechAUTHORS:20171128-142213688
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Official Citation:Thoutireddy, P., Molinari, J. F., Repetto, E. A. and Ortiz, M. (2002), Tetrahedral composite finite elements. Int. J. Numer. Meth. Engng., 53: 1337–1351. doi:10.1002/nme.337
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83544
Deposited By: Lydia Suarez
Deposited On:28 Nov 2017 22:31
Last Modified:24 Feb 2020 10:30

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