Towards poroelasticity of fractal materials

This study proposes a model of poroelasticity grasping the fractal geometry of the pore space occupied by the fluid phase as well as the fractal geometry of the solid (matrix) phase. The dimensional regularization approach employed is based on product measures which account for an arbitrary anisotropic structure. This, in turn, leads to a re-interpretation of spatial gradients (of both fluid velocity and displacement fields) appearing in the balance and constitutive equations; the latter are adapted from the classical poroelasticity. In effect, an initial-boundary value problem of a fractal medium can be mapped into one of a homogenized, non-fractal medium, and, should all the fractal dimensions become integer, all the equations reduce back to those of classical poroelasticty. Overall, the proposed methodology broadens the applicability of continuum mechanics/physics and sets the stage for poromechanics of fractal materials.