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<p>To enable the numerical simulation of complex time-dependent multi-body contact problems, a class of generalized variational inequality models is formulated. Subsequently, the corresponding temporally semi-discrete and fully discrete problems are formulated. Under general hypotheses, the unique solvability of the numerical solutions is established, and error estimates are derived. The relevant results are applied to analyze the approximation properties of the finite element numerical solutions for a class of history-dependent multi-layer contact systems, and the convergence rate is established under general hypotheses. Such multi-layer contact systems hold extensive application value in engineering mechanics analyses, such as those for asphalt pavements. The final numerical simulation experiments validate the theoretical analysis results regarding the convergence rate of the numerical solutions, while also demonstrating the feasibility of analyzing such complex multi-body contact problems within the framework of variational inequalities.</p>

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Numerical Analysis for Time-Dependent Variational Inequalities and Their Application in Multi-Layer Contact Systems

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Zhizhuo Zhang,
  • Mikaël Barboteu,
  • Zhao-Dong Xu,
  • Jinde Cao

摘要

To enable the numerical simulation of complex time-dependent multi-body contact problems, a class of generalized variational inequality models is formulated. Subsequently, the corresponding temporally semi-discrete and fully discrete problems are formulated. Under general hypotheses, the unique solvability of the numerical solutions is established, and error estimates are derived. The relevant results are applied to analyze the approximation properties of the finite element numerical solutions for a class of history-dependent multi-layer contact systems, and the convergence rate is established under general hypotheses. Such multi-layer contact systems hold extensive application value in engineering mechanics analyses, such as those for asphalt pavements. The final numerical simulation experiments validate the theoretical analysis results regarding the convergence rate of the numerical solutions, while also demonstrating the feasibility of analyzing such complex multi-body contact problems within the framework of variational inequalities.