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

Summary

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.

Abstract

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