Cone complimentary-based numerical manifold method modeling frictional and cohesive contact problems

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.