Modeling Deformable Porous Media with Peridynamics

We propose a peridynamic model for porous materials that can deform and fracture under different loading conditions. Traditional continuum methods use differential operators, which are unable to model materials with cracks or other discontinuities. However, peridynamics can simulate these types of materials because it uses an integral operator to model the material's constitutive relationship between stress and strain. The points within small regions of the material interact following a prescribed nonlocal interaction law. We implement our models in a new software package called ParticLS, where the materials are treated as bonded particles and the sum of forces acting on each particle approximates the peridynamic integral operator.

To simulate porous materials, we explicitly model the material pores with a repulsive peridynamic interaction law that limits the proximity of particles to each other. This model follows traditional peridynamic laws, allowing the body of particles to deform and fracture---simulating the mechanics of porous materials. We demonstrate our model by applying a known force to a porous plate as particulate matter passes through it. We relate the model parameter controlling pore size to the flux of the particulate matter. ParticLS can simulate a variety of particulate geometries, which allows us to simulate realistic materials with different pore structures.