  We combine classical continuum mechanics with the recently developed calculus
for mixed-dimensional problems to obtain governing equations for flow in, and
deformation of, fractured materials. We present models both in the context of
finite and infinitesimal strain, and discuss non-linear (and
non-differentiable) constitutive laws such as friction models and contact
mechanics in the fracture. Using the theory of well-posedness for evolutionary
equations with maximal monotone operators, we show well-posedness of the model
in the case of infinitesimal strain and under certain assumptions on the model
parameters.
