Simulation of hyperelastic materials in real-time using deep learning.

Area of Science:

• Computational Mechanics
• Artificial Intelligence
• Numerical Methods

Background:

• The finite element method (FEM) is crucial for engineering but computationally expensive.
• Existing methods to reduce FEM computation time include domain decomposition, parallel computing, adaptive meshing, and model order reduction.
• There is a need for efficient methods to handle complex, non-linear problems in computational mechanics.

Purpose of the Study:

• To introduce U-Mesh, a data-driven deep learning method utilizing a U-Net architecture.
• To approximate the non-linear relationship between contact forces and displacement fields in FEM.
• To demonstrate the enhancement of computational mechanics through compact encoding of non-linear models using deep learning.

Main Methods:

• Development of U-Mesh, a novel data-driven method based on a U-Net architecture.
• Application of U-Mesh to benchmark engineering problems: a cantilever beam, an L-shape, and a liver model.
• Comparative analysis of U-Mesh against proper orthogonal decomposition (POD) for simulation accuracy and speed.

Main Results:

• U-Mesh effectively approximates non-linear relations in FEM simulations.
• The method achieves very fast simulation times across diverse geometries, topologies, and mesh resolutions.
• U-Mesh demonstrates high accuracy with minimal errors, comparable or superior to POD.

Conclusions:

• Deep learning, via U-Mesh, offers a powerful enhancement for computational mechanics.
• U-Mesh provides a computationally efficient and accurate alternative for solving complex engineering problems.
• The U-Mesh method shows significant potential for accelerating simulations in various engineering applications.