Abstract An unconditionally stable cone complementary formulation is established in this study for modeling frictional and cohesive contact problems. In order to simulate continuous and discontinuous media within a unified framework, the proposed cone complementary formulation is further integrated into the high-order numerical manifold method (NMM), which is based on six-node triangular meshes and is free from rank deficiency issue associated with some high-order formulas. Such that, the use of penalty parameters as well as the open-close iteration adopted by the original NMM can be avoided. Some numerical examples are designed to demonstrate that the proposed high-order NMM can not only preserve fundamental conservation laws of the system, but also maintain accuracy and robustness in solving frictional and cohesive contact problems.

中文翻译：

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基于锥体互补的数值流形方法模拟摩擦和内聚接触问题

摘要 本研究建立了一个无条件稳定锥互补公式，用于模拟摩擦和内聚接触问题。为了在统一框架内模拟连续和不连续介质，将所提出的锥互补公式进一步集成到基于六节点三角形网格的高阶数值流形方法 (NMM) 中，并且没有相关的秩不足问题用一些高阶公式。这样，可以避免使用惩罚参数以及原始 NMM 采用的开闭迭代。一些数值例子旨在证明所提出的高阶 NMM 不仅可以保留系统的基本守恒定律，而且在解决摩擦和内聚接触问题时也能保持准确性和鲁棒性。