Tetrahedral composite finite elements

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 whileat thesametime , minimizing thenumbe r 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 -ve-point quadrature rule. The element passes the patch test in arbitrarily distorted con-gurations. 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 veri-ed that the element satis-es the Babu@ska–Brezzi condition for a regular mesh con-guration. 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 Aow