Abstract
AbstractA new family of hybrid/mixed finite elements optimized for numerical stability is introduced. It comprises a linear hexahedral and quadratic hexahedral and tetrahedral elements. The element formulation is derived from a consistent linearization of a well-known three-field functional and related to Simo–Taylor–Pister () elements. For the quadratic hexahedral and tetrahedral elements we derive (static reduced) discontinuous hybrid elements, as well as continuous mixed finite elements with additional primary unknowns for the hydrostatic pressure and the dilation, whereas the linear hexahedral element is of the discontinuous type. The elements can readily be used in combination with any isotropic, invariant-based hyperelastic material model and can be considered as being locking-free. In a representative numerical benchmark test the elements numerical stability is assessed and compared to -elements and the family of discontinuous hybrid elements implemented in the commercial finite element code Abaqus/Standard. The new elements show a significant advantage concerning the numerical robustness.
Funder
Deutsches Institut für Kautschuktechnologie e.V.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Mechanical Engineering,Ocean Engineering,Computational Mechanics
Cited by
6 articles.
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