Effective double-poroelasticity derived via homogenization of two non-interacting solid phases percolated by a viscous fluid

Abstract

This work carries out the derivation of the governing equations for a composite material that has the following microstructure. Our microstructure possesses an elastic matrix that has an incompressible Newtonian fluid flowing in the pores and then the latter is additionally reinforced by an elastic network that is fully surrounded by the fluid. We exploit the length scale separation that exists in the system between the microscale and the overall size of the material to apply the asymptotic homogenization technique. The resulting model comprises additional terms and equations to account for the discontinuity between the elastic phases, and reduces to more standard poroelastic formulations only when the two elastic phases are in contact. The coefficients of the novel model are to be computed by solving appropriate periodic cell differential problems. The coefficients encode the details of the geometry and stiffness of the microstructure. The model is applicable to a variety of scenarios, such as artificial constructs and biomaterials.