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)

翻译：接触力学数值方法在工程应用中具有重要意义，能够预测和分析各种条件下复杂的表面相互作用。本文提出一种基于能量的物理信息神经网络（PINNs）框架，用于求解大变形条件下的无摩擦接触问题。受微观Lennard-Jones势启发，采用表面接触能量描述接触现象。为确保所提PINN框架的鲁棒性，引入了松弛、渐进加载和输出缩放技术。在数值算例中，通过经典的赫兹接触基准问题验证了所提PINN框架的有效性与鲁棒性。此外，测试了考虑几何与材料非线性的挑战性接触问题。结果表明，所提PINN框架为非线性接触力学提供了可靠而强大的分析工具。更重要的是，在处理复杂接触问题时，该框架展现出与商业有限元软件相当的计算效率。本文所用代码公开于https://github.com/JinshuaiBai/energy_PINN_Contact（代码将在论文录用后开放）。