Energy-based physics-informed neural network for frictionless contact problems under large deformation

TL;DR

This paper introduces an energy-based physics-informed neural network framework for solving complex frictionless contact problems under large deformation, demonstrating robustness, accuracy, and computational efficiency in nonlinear contact mechanics.

Contribution

The paper presents a novel energy-based PINNs approach incorporating microscopic potential inspired contact modeling, with techniques to enhance robustness for large deformation contact problems.

Findings

Successfully applied to Hertz contact benchmark problem

Effective for geometrically and materially nonlinear contact problems

Achieves competitive computational efficiency with FEM software

Abstract

Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINNs) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINNs framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINNs framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINNs framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at https://github.com/JinshuaiBai/energy_PINN_Contact.(The code will be available after acceptance)