  A novel regularized fracture model for crack propagation in porous media is
proposed. Our model is obtained through homogenization theory and formal
asymptotic expansions. We start with a regularized quasi-static fracture model
posed in a periodically perforated domain obtained by periodic extension of a
re-scaled unit cell with a hole. This setup allows us to write two separated
minimality conditions for the primary (displacement) and secondary variables
plus a balance of energy relation. Then we apply the usual asymptotic expansion
matching to deduce limit relations when the re-scaling parameter of the unit
cells vanishes. By introducing cell problems solutions and a homogenized tensor
we can recast the obtained relations into a novel model for crack propagation
in porous media. The proposed model can be interpreted as a regularized
quasi-static fracture model for porous media. This model yields two separated
(homogenized) minimality conditions for the primary and secondary variables and
a balance of homogenized energy relation.
