A strong-form meshfree collocation method for modeling stationary cracks with frictional contact

We present a strong-form meshfree collocation method for frictional contact of two deformable bodies within the context of frictional crack problems. The method inherently achieves desirable features of meshfree methods by completely avoiding the construction of meshes or grids, such that the only required numerical approximation units are nodes (used as collocation points). For the recognition of a contact or crack surface, a line segment is used without any connection with the node structure. A contact constraint due to two body frictional contact is implemented in the strong-form meshfree discretization. Since the contact boundary is a Neumann boundary, it contributes to the system of equations as a traction boundary condition, but it does not yield extra unknowns. Although the material is linear elastic, the presence of the constraint formulation leads to an iterative nonlinear solution procedure. The assembled discrete system generates a consistent and stable solution despite the presence of contact constraints and the crack discontinuity, because the constraint formulation and crack modeling are well combined with the strong-form meshfree collocation method. Numerical experiments demonstrate the robustness and consistency of the method through comparison with analytical and finite element solutions.