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

Area of Science:

• Computational mechanics
• Solid mechanics
• Finite element analysis

Background:

• Large strain, polyconvex, nearly incompressible elasticity simulations face challenges with accuracy, robustness, and efficiency.
• Locking phenomena in computational formulations hinder precise simulations of material behavior.

Purpose of the Study:

• To present two novel computational methods for overcoming locking phenomena in nearly incompressible elasticity.
• To enhance the accuracy, robustness, and computational efficiency of large strain simulations.

Main Methods:

• A displacement-pressure formulation utilizing a stable finite element pairing with bubble functions.
• A pressure-projection stabilized P1-P1 finite element pair for simplified stabilization.

Main Results:

• Both proposed methods effectively mitigate locking phenomena in simulations.
• Benchmark results confirm the robustness and computational efficiency of the presented approaches.
• The methods demonstrate versatility, applicability to various finite elements, and generalization to transient dynamics.

Conclusions:

• The developed methods offer significant improvements for simulating nearly and fully incompressible materials.
• These techniques provide a robust and computationally efficient alternative for complex elasticity problems.
• The versatility of the methods allows for broad application across different finite element types and dynamic scenarios.