Mean‐strain 10‐node tetrahedron with energy‐sampling stabilization for nonlinear deformation

Abstract

SummaryA mean‐strain 10‐node tetrahedral element is developed for the solution of geometrically nonlinear solid mechanics problems using the concept of energy‐sampling stabilization. A uniform‐strain tetrahedron for applications to linear elasticity was recently described. The formulation as extended here is able to solve large‐strain hyperelasticity. The present 10‐node tetrahedron is composed of several four‐node linear tetrahedral elements, four tetrahedra in the corners, and four tetrahedra that tile the central octahedron in three possible sets of four‐node tetrahedra, corresponding to three different choices for the internal diagonal. We formulate a mean‐strain element with stabilization energy evaluated on the four corner tetrahedra, which is shown to guarantee consistency and stability. The stabilization energy is expressed through a stored‐energy function, and contact with input parameters in the small‐strain regime is made. The neo‐Hookean model is used to formulate the stabilization energy. As for small‐strain elasticity, the stabilization parameters are determined by actual material properties and geometry of a tetrahedra without any user input. The numerical tests demonstrate that the present element performs well for solid, shell, and nearly incompressible structures. Copyright © 2016 John Wiley & Sons, Ltd.