  Simulating the deformation of fractured media requires the coupling of
different models for the deformation of fractures and the formation surrounding
them. We consider a cell-centered finite-volume approach, termed the multipoint
stress approximation (MPSA) method, which is developed in order to discretize
coupled flow and mechanical deformation in the subsurface. Within the MPSA
framework, we consider fractures as co-dimension one inclusions in the domain,
with the fracture surfaces represented as line pairs in 2D (faces in 3D) that
displace relative to each other. Fracture deformation is coupled to that of the
surrounding domain through internal boundary conditions. This approach is
natural within the finite-volume framework, where tractions are defined on
surfaces of the grid. The MPSA method is capable of modeling deformation
considering open and closed fractures with complex and nonlinear relationships
governing the displacements and tractions at the fracture surfaces. We validate
our proposed approach using both problems for which analytical solutions are
available and more complex benchmark problems, including comparison with a
finite-element discretization.
