A stabilised displacement–volumetric strain formulation for nearly incompressible and anisotropic materials

Abstract

The simulation of structural problems involving the deformations of volumetric bodies is of paramount importance in many areas of engineering. Although the use of tetrahedral elements is extremely appealing, tetrahedral discretisations are generally known as very stiff and are hence often avoided in typical simulation workflows.The development of mixed displacement–pressure approaches has allowed to effectively overcome this problem leading to a class of locking-free elements which can effectively compete with hexahedral discretisations while retaining obvious advantages in the mesh generation step. Despite such advantages the adoption of the technology within commercial codes is not yet pervasive.This can be attributed to two different reasons: the difficulty in making use of standard constitutive libraries and the implied continuity of the pressure, which makes the application of the method questionable in the context of multi-material problems. Current paper proposes the adoption of the volumetric strain instead of the pressure as a nodal value. Such choice leads to the definition of a modified strain making the use of standard strain-driven constitutive laws straightforward. At the same time, the continuity of the volumetric strain across multimaterial interfaces can be understood as a sort of kinematic constraint (stresses can still remain discontinuous across material interfaces). The new element also opens the door to the use of anisotropic constitutive laws, which are typically problematic in the context of mixed elements.