A robust hybrid‐element family for strongly compressed hyperelastic materials

Technical elastomers are usually quasi‐incompressible. For simulations they are, therefore, often modeled as ideal incompressible hyperelastic materials, or a linear relation between the hydrostatic pressure and the (volumetric) dilation is assumed, i.e., a linear compression model with constant bulk modulus is used. However, for strongly compressed structural components, like sealings or damper elements, a nonlinear compression model might be required as well, in order to achieve accurate results. In general, the numerical ill‐posedness of irreducible (purely displacement‐based) finite element formulations for quasi‐incompressible materials demands for a hybrid/mixed finite element implementation. State of the art hybrid/mixed‐elements still suffer from numerical stability issues that can be greatly amplified by the usage of nonlinear compression models. In the talk, a robust hybrid‐element family is introduced that can readily be used in combination with any isotropic, invariant‐based hyperelastic material model. The mesh convergence behavior and the numerical stability of the new element family are assessed by benchmark testing and compared to classical Simo‐Taylor‐Pister (STP) elements as well as the hybrid‐element family (C3D8H, C3D20H, C3D10H) implemented in the commercial finite element code Abaqus Standard, Simulia (Dassault Systèmes). The presented finite element family is free of volumetric locking and more robust than STP or Abaqus hybrid‐elements, especially in combination with strongly nonlinear compression models.