A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects

Area of Science:

• Computational mechanics
• Numerical analysis
• Finite element analysis

Background:

• Simulating cuts in deformable bodies is computationally intensive.
• Existing methods struggle with high resolution and efficiency.
• Adaptive mesh refinement and multigrid methods offer potential improvements.

Purpose of the Study:

• To develop a computationally efficient hexahedral finite element method for simulating cuts in deformable bodies.
• To integrate adaptive element refinements and topological changes into a geometric multigrid solver.
• To achieve high-resolution simulations of cutting processes.

Main Methods:

• A hexahedral finite element method with corotational strain formulation.
• Embedding adaptive element refinements and topological changes into a geometric multigrid solver.
• Duplicating coarse grid cells to represent discontinuities and adapting the splitting cubes algorithm.

Main Results:

• The proposed method achieves high computational efficiency and physical accuracy.
• Simulations of cutting deformable bodies at very high resolutions are enabled.
• The approach effectively handles adaptive refinement and topological changes within the multigrid framework.

Conclusions:

• The developed finite element method provides an efficient and accurate solution for simulating cuts in deformable bodies.
• The integration of adaptive mesh refinement and multigrid solvers is key to achieving high-resolution results.
• This method advances the capabilities for simulating complex mechanical deformations and cutting processes.