INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2002; 53:1337–1351 (DOI: 10.1002/nme.337) Tetrahedral composite nite elements P. Thoutireddy, J. F. Molinari, E. A. Repetto and M. Ortiz *; † Graduate Aeronautical Laboratories; California Institute of Technology; Pasadena; CA 91125; U.S.A. SUMMARY 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 dened over the entire domain of the composite element. The element is designed to have well-dened lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of vol- ume 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 ve-point quadrature rule. The element passes the patch test in arbitrarily distorted congurations. Our numerical tests demonstrate that CT el- ement 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 veried that the element satises the Babu ska–Brezzi condition for a regular mesh congu- ration. 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 unconned plastic ow. Copyright ? 2001 John Wiley & Sons, Ltd. KEY WORDS: nite element analysis; composite element; contact; dynamics; inf–sup test 1. INTRODUCTION Camacho and Ortiz [1; 2] briey described the triangular and tetrahedral elements constructed by assembling linear subtriangles and tetrahedra and coupling them to a continuous linear strain eld over the assemblage. They called these elements composite triangular and tetra- hedral, or CT, elements. The advantages of these elements arise primarily in explicit time integration and contact-impact problems, where the lumped mass of their midside nodes is well matched to their corner node masses. This feature eectively overcomes the diculties inherent to quadratic simplicial elements, for which the row-sum method of lumping results in zero or negative corner masses. Furthermore, the volumetric locking which characterizes * Correspondence to: Michael Ortiz, Graduate Aeronautical Laboratories, California Institute of Technology, Firestone Flight Sciences Laboratory, MS-105-50, Pasadena, CA 91125, U.S.A. † E-mail: ortiz@aero.caltech.edu Contract=grant sponsor: Department of Energy, U.S.A. Received 14 August 2000 Copyright ? 2001 John Wiley & Sons, Ltd. Revised 9 February 2001