Mixed/Hybrid finite elements for finite deformations of quasi‐incompressible materials with non‐constant bulk moduli

Technical elastomers are usually quasi‐incompressible. For simulations they are, therefore, often modeled as ideal incompressible or a linear relation between the hydrostatic pressure and the (volumetric) dilation is assumed, i.e., a constant bulk modulus. However, for strongly compressed structural components, like sealings or damper elements, a nonlinear material model for the compression behavior is required in order to achieve accurate results. In general, the numerical ill‐posedness of irreducible (purely displacement‐based) finite element (FE) 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 versatile mixed/hybrid finite element family for finite deformations is introduced that can readily be used in combination with any invariant‐based hyperelastic material model. The numerical stability is assessed by a benchmark test and compared to other established hybrid elements. The presented finite element family is way robuster than comparable hybrid elements implemented in the commercial FE‐code Abaqus Standard, Simulia (Dassault Systèmes).