Tetrahedral composite finite elements

By P. Thoutireddy, Jean-François Molinari, E. A. Repetto, Magdalena Ortiz. International Journal for Numerical Methods in Engineering, 2002

52 citations recorded by the source corpus.

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. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a6b10f4920a6e9d6c560eea666bac9a9524184c2

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Citations in the corpus

A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models (2007, unknown): “In addition, Thoutireddy et al. (2002) have developed a composite tetrahedral finite element composed of twelve four-node linear tetrahedral elements with an assumed linear displacement field in each tetrahedral element.”
A new three-dimensional interface finite element to simulate fracture in composites (2004, methodology): “In the case of the modified interface element, the quadratic triangle is subdivided into four linear triangles, as shown on Fig. 10. The shape functions at ðn;gÞ depend on the particular subtriangle in which the point is located, and they are expressed by ( Thoutireddy et al., 2002 ),”