The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
[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/mix...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/186461 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/186461 |
| Access Level: | acceso abierto |
| Palabra clave: | Hybrid finite element Mixed formulation Finite deformation Hyperelasticity Rubber-like material Quasi-incompressible material Discontinuous finite element |
| Sumario: | [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]. |
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