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<p>In this study, we investigate the deep learning (DL) approach to elastic contact problems with boundary conditions such as Signorini, Tresca friction, Coulomb friction, and non-convex non-smooth subgradient-type conditions, in the framework of the deep Ritz method (DRM). We design loss functions with hard and soft constraints. For Coulomb-friction condition, we apply the penalty-regularization approach and an iterative algorithm to minimize the unknown-dependent loss function. We conduct massive numerical experiments to investigate the applicability of our methods. Additionally, we compare the performance of the DRM with the finite element methods (FEMs) for 3D contact problems.</p>

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The deep Ritz methods for the elastic contact problems with the Signorini, Tresca-friction, Coulomb-friction, and non-convex non-smooth subgradient-type boundary conditions

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Tongtong Wang,
  • Longteng Hu,
  • Guanyu Zhou,
  • Ping Zeng,
  • Yicheng Ren

摘要

In this study, we investigate the deep learning (DL) approach to elastic contact problems with boundary conditions such as Signorini, Tresca friction, Coulomb friction, and non-convex non-smooth subgradient-type conditions, in the framework of the deep Ritz method (DRM). We design loss functions with hard and soft constraints. For Coulomb-friction condition, we apply the penalty-regularization approach and an iterative algorithm to minimize the unknown-dependent loss function. We conduct massive numerical experiments to investigate the applicability of our methods. Additionally, we compare the performance of the DRM with the finite element methods (FEMs) for 3D contact problems.