An Explicit Geometrically-Nonlinear Discretization of the 3-D Tetrahedral Element

Abstract

An actual discretization is presented for the 3-D tetrahedral element in large displacements. After a decomposition of the total freedom of that element into parameters of position-as-a-rigid-body and those of deformation, the strain-constant interpolation is applied to the defined deformation. The geometrical decompositions and the associated force transformations are developed physically in explicit form. While the material is assumed elastic for finite strains, any geometrically nonlinear effects are taken into account, systematically and rigorously.