Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics

TL;DR

This paper introduces two versatile stabilized finite element methods for nearly and fully incompressible solid mechanics, improving accuracy and efficiency while avoiding locking phenomena in large strain elasticity simulations.

Contribution

The paper presents two novel stabilized finite element formulations that are adaptable to various element types and extend to dynamic problems, enhancing robustness and computational performance.

Findings

Both methods effectively prevent locking in incompressible elasticity simulations.

The approaches are verified against standard benchmarks, demonstrating robustness.

Methods are computationally efficient and versatile for different finite element types.

Abstract

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using a stable finite element pairing with bubble functions, and another one using a simple pressure-projection stabilized P1-P1 finite element pair. A key advantage is the versatility of the proposed methods: with minor adjustments they are applicable to all kinds of finite elements and generalize easily to transient dynamics. The proposed methods are compared to and verified with standard benchmarks previously reported in the literature. Benchmark results demonstrate that both approaches provide a robust and computationally efficient way of simulating nearly and fully incompressible materials.