A scaled boundary finite element method for modelling crack face contact problems

In the case of arbitrary traction on the side faces of an object, a polynomial function of the radial coordinate can be employed to describe the side-face loads using the scaled boundary finite element method (SBFEM). A SBFEM shape function considering the side-face loads is presented together with the corresponding stiffness matrix and equivalent node load. The Lagrange multiplier method is used to establish the contact model between the crack faces. The elements corresponding to the crack faces are divided into non-crack-tip elements and crack-tip elements. For the former, the crack is designated the boundary of the polygonal SBFEM element; the contact tractions on the boundary are assigned to the nodes where the Lagrange multiplier is applied for the point constraints. For the latter, the Lagrange multiplier is assumed to be linear on the side faces for the segment constraints. Numerical examples demonstrate the validity of the proposed SBFEM in addressing the crack face contact problem.