The virtual element method for rock mass with frictional cracks

This paper presents the frictional contact formulation for frictional crack in elastic solids at small strains based on the Penalty method in the framework of the virtual element method. For normal direction of contact interface, the Karush-Kuhn-Tucker conditions (or KKT-conditions) is engaged to handle the contact problem. The Coulomb's law is exerted to respond to the crack interface's stick-slip condition for the tangential direction of the contact interface. The frictional contact constraints are forced by the classical Penalty method and the node-tosegment approach is applicated to compute the contact element on the contact interface. Several numerical examples with Voronoi meshes are offered to display the contact algorithm accuracy compared with existing results in the imitation of a variety of contact conditions. In the last numerical simulations, the contact algorithm is also suitable for the rock mass with multiple cracks.

Automated summary

This paper presents a frictional contact formulation for frictional crack in elastic solids at small strains based on the Penalty method in the virtual element method framework. The Karush-Kuhn-Tucker conditions are used for normal direction of contact interface, while Coulomb's law is applied for the tangential direction. Contact constraints are enforced using the Penalty method, and the algorithm is suitable for rock masses with multiple cracks, shown through numerical examples.