A numerical framework coupling finite element and meshless methods in sequential and parallel simulations.

Area of Science:

• Computational Mechanics
• Numerical Methods in Engineering

Background:

• The Finite Element Method (FEM) faces challenges with excessive element deformation in large deformation problems.
• Dynamic remeshing, a common solution, is hindered by computational expense, numerical noise, and geometric limitations.
• Meshless Methods (MM) avoid mesh connectivity issues but are computationally intensive compared to FEM.

Purpose of the Study:

• To present a novel numerical framework combining FEM and MM to address large deformation scenarios efficiently.
• To maintain computational efficiency by strategically applying MM only to regions with significant deformation.
• To enhance the parallelization capabilities of MM for improved computational speed-up.

Main Methods:

• A hybrid FEM-MM scheme coupling both discretization methods within a single problem.
• MM is applied to sensitive regions, while FEM handles less distorted areas.
• A simplified MM parallelization strategy leveraging maximum entropy approximation and domain convexification.
• A quadrature point-driven approach for method-agnostic treatment of constitutive models and assembly.

Main Results:

• The proposed framework demonstrates excellent scalability for large deformation problems.
• Achieves a favorable balance between simulation accuracy and computational cost.
• The method-agnostic assembly and simplified parallelization contribute to computational efficiency.

Conclusions:

• The hybrid FEM-MM approach offers an effective solution for simulating large deformations.
• It overcomes limitations of traditional FEM and computationally expensive MM.
• The framework provides a computationally efficient and scalable tool for complex engineering simulations.