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.
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