Construction of a peridynamic model for viscous flow

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation mass and momentum. This is nonlocal, different models that utilize numerical methods like, e.g., so-called “peridynamic differential operator” to approximate solutions classical Navier-Stokes equations. show continuity equation limiting case PD one, assuming certain smoothness conditions. The calibrated by enforcing linear consistency stress term with Couette Poiseuille flows, incompressible fluid past regular lattice cylinders are used verify new formulation, at low Reynolds numbers. constructive approach in deriving allows seamless coupling corrosion or fracture simulating complex fluid-structure interaction problems which solid degradation takes place, such as erosion-corrosion, hydraulic fracture, etc. Moreover, sheds light on relationships between local nonlocal models.