The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids

Abstract

[EN] We revisit the well-known three-field formulation introduced by Simo and Taylor, [5]. However, while in [5] a semi-discretization is used to eliminate the additional primary unknowns before the problem is linearized in terms of the not yet discretized displacement field, we introduce hybrid/mixed elements based directly on the consistent linearization of the threefield formulation on the continuum-level. In the latter case, static condensation is used to eliminate the additional unknowns on the element-level after the linearization of the continuum formulation in order to derive discontinuous hybrid-elements. A family of Simo-Taylor-Pister (STP) elements, as well as a family of elements based on the continuum-level linearization (CL3F), designed to coincide in terms of the interpolation schemes, the number of assembled degrees of freedom and the number of integration points with the Abaqus hybrid-elements (C3D8H,C3D20H,C3D10H) are compared to those elements by benchmark tests. Material parameters were obtained by least-square fitting to experimental data of an industrial NR/IR-blend (natural rubber / isoprene rubber) used for damping applications. All tested elements are free of volumetric locking. The STP-elements show severe stability issues. In general the maximum stable step-width of the Abaqus hybrid-elements is higher in comparison to the STP-elements. However, the CL3F-elements outperform the Abaqus elements in general without the usage of numerical stabilization. Especially in combination with strongly nonlinear compression models, the advantage of the CL3F-elements is huge – here the stable step-width is up to 22 times larger. Details can be found in a contribution which is currently under review, [7].