This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output transformations, to enforce Dirichlet and Neumann boundary conditions as hard constraints. The inherent inequality constraints in contact mechanics, particularly the Karush-Kuhn-Tucker (KKT) conditions, are addressed as soft constraints by integrating them into the network's loss function. To enforce the KKT conditions, we leverage the nonlinear complementarity problem (NCP) approach, specifically using the Fischer-Burmeister function, which is known for its advantageous properties in optimization. We investigate two benchmark examples of PINNs in 3D contact mechanics: a single contact patch test and the Hertzian contact problem.

翻译：本文探讨了物理信息神经网络（PINNs）在三维接触力学正问题中的应用，重点关注小变形弹性问题。我们采用一种混合变量公式，并通过输出变换增强，以将狄利克雷和诺伊曼边界条件作为硬约束强制执行。接触力学中固有的不等式约束，特别是卡鲁什-库恩-塔克（KKT）条件，通过将其整合到网络的损失函数中作为软约束处理。为强制执行KKT条件，我们利用非线性互补问题（NCP）方法，具体采用了费舍尔-伯迈斯特函数，该函数在优化中以其优越特性而闻名。我们研究了PINNs在三维接触力学中的两个基准算例：单接触面片测试和赫兹接触问题。