A Mixed Finite Element Formulation for Arbitrary Element Geometries and Nearly-Incompressible Finite Elasticity

European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS)

Abstract

In this contribution, the displacement-based scaled-boundary finite element method (SBFEM) is extended to a mixed displacement-pressure formulation for the geometrically and materially nonlinear analysis of nearly-incompressible solids. The displacements and pressures are both parameterized by a scaled-boundary approach, for which an interpolation in the scaling direction is used. Here, higher-order interpolation functions may be employed. It is shown that by introducing the pressure as a field variable, volumetric locking is no longer present. The approach is valid for arbitrary scaling center locations, which can be either inside or outside of the element domain. Other than that, the formulation is valid for non-star-convex element geometries. Numerical examples show that the method is capable of alleviating volumetric locking for arbitrary polygonal meshes and is beneficial in comparison to the displacement-based method when it comes to modeling nearly-incompressible materials.

Authors 3

1. B. Sauren corresponding Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52062 Aachen , Germany

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52062 Aachen, Germany

2. S. Klarmann Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52062 Aachen , Germany

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52062 Aachen, Germany

3. S. Klinkel Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52062 Aachen , Germany

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52062 Aachen, Germany