A smoothed meshfree method for simulation of frictional embedded discontinuities

Abstract An enriched cell-based smoothed point interpolation method (CSPIM) is presented in this study for the numerical modelling of domains including weak and strong discontinuities. A triangular background mesh is used for domain discretisation in the proposed method. The arbitrary discontinuities, such as material interfaces and cracks, are considered in the numerical formulation by enhancing the approximation of the displacement field using appropriate enrichment functions in the vicinity of the existing discontinuity. The contact condition of strong discontinuities is introduced through satisfaction of the Kuhn–Tucker inequalities, also known as the active set strategy. The stick–slip behaviour in the tangential direction of the contact is described through the Coulomb’s friction law. Contrary to the traditional contact algorithms (e.g., node-to-segment and segment-to-segment), the contact kinematics are satisfied within the elements, and not at the boundary of the elements, substantially facilitating the implementation of the contact algorithm. Furthermore, the proposed formulation eliminates the need for costly partitioning of the elements intersected by the discontinuity, which is often required for numerical integration in the XFEM. The enriched CSPIM is applied to the governing equation of the fractured domain to obtain the spatially discretised form of the governing equations. A Newton-Raphson scheme is adopted to deal with nonlinearities arising from the possible contact condition. Two numerical examples are presented to demonstrate the application of the proposed approach.