A New Contact Formulation for Large Frictional Sliding and Its Implement in the Explicit Numerical Manifold Method

Modelling discontinuous systems involving large frictional sliding is one of the key requirements for numerical methods in geotechnical engineering. The contact algorithms for most numerical methods in geotechnical engineering is based on the judgement of contact types and the satisfaction of contact conditions by the open–close iteration, in which penalty springs between contacting bodies are added or removed repeatedly. However, the simulations involving large frictional sliding contact are not always convergent, particularly in the cases that contain a large number of contacts. To avoid the judgement of contact types and the open–close iteration, a new contact algorithm, in which the contact force is calculated directly based on the overlapped area of bodies in contact and the contact states, is proposed and implemented in the explicit numerical manifold method (NMM). Stemming from the discretization of Kuhn–Tucker conditions for contact, the equations for calculating contact force are derived and the contributions of contact force to the global iteration equation of explicit NMM are obtained. The new contact algorithm can also be implemented in other numerical methods (FEM, DEM, DDA, etc.) as well. Finally, five numerical examples are investigated to verify the proposed method and illustrate its capability.