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

2024-11-06

arXiv.org

AI Summary

Addressing the challenges of modeling large-deformation, frictionless contact—particularly on complex curved surfaces—and the poor convergence of traditional physics-informed neural networks (PINNs), this work proposes an energy-variational PINN framework. Methodologically, it innovatively incorporates a Lennard-Jones-type surface contact potential function into the PINN formulation, marking the first integration of microscopic interfacial potential concepts to characterize contact mechanics. To enhance robustness, a multi-level stabilization strategy is introduced, comprising relaxation mechanisms, progressive loading, and output-adaptive scaling—significantly improving convergence and generalization for strongly nonlinear contact problems. Validated against the Hertz benchmark and multiple challenging nonlinear contact cases, the method achieves accuracy comparable to finite element methods (FEM) while attaining computational efficiency on par with commercial FEM software. The implementation is publicly available.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Low Level & Physics-based Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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)

Problem

• Frictionless Contact
• Large Deformation
• Complex Surface Analysis

Innovation

• Energy-based Neural Network
• Nonlinear Contact Mechanics
• High Efficiency and Accuracy