Numerical study of the breakup of a porous medium due to fluid dynamic forces

The present manuscript treats the breakup of porous media due to the action of fluid dynamic forces. The problem of the interaction between solid structures and fluid flows, named Fluid-Structure Interaction (FSI), is a problem that interests a wide range of engineering applications and scientific fields, from aerospace, civil and biomedical engineering to geotechnics and planetary sciences. This phenomenon is often associated with hydraulic fracture due to fluid-dynamic forces, which act on immersed solids. To reproduce the phenomenon correctly fluid dynamics, solid mechanics and fracture mechanics have to be simultaneously considered. The major difficulty of the classical theories of solid mechanics is to predict and simulate the formation of cracks due to the arising of singularities in the derivatives of partial differential equations where discontinuities form. The present manuscript intends to employ a novel numerical method to address FSI with solid fracturing of a porous medium, where solid and fracture mechanics are simulated with peridynamic, a well-established reformulation of continuum theory which, replacing partial differential equations with integral ones, intrinsically accounts for crack formation and branching. Instead, the dynamic of the fluid phase is reproduced by the three-dimensional incompressible formulation of the Navier-Stokes equations by using Direct Numerical Simulations (DNS). Then, the Immersed Boundary Method (IBM) is used to impose wall boundary conditions on the fluid-solid interfaces. The simulations are run by using a massively parallel solver, written in Fortran 90 extended with a Message-Passing Interface (MPI) standard, which has been previously developed and validated. In the present manuscript, this new numerical tool has been employed to simulate the deformation and fragmentation of a linear-elastic porous medium. Three different simulations have been performed: the first reproduces the deformation of solid without fracture, the second with partial fracture and the third with total fracture. Then the comparisons between stress and strain distributions, before and after the fracturing process, are reported and discussed for all the three cases listed above. Furthermore, for these distributions, a failure criterion, which tries to predict when the fracture occurs, is presented. In addition, for all cases, the trend over time of the pressure drop, change in porosity and permeability are reported and discussed.