Sand, ballast, cement clinker, pharmaceutical granules: assemblies whose bulk behavior comes from what individual grains do to each other. The standard tool for simulating them, the discrete element method, treats each particle as rigid and puts all the physics in the contact law between them. That is an excellent approximation right up until the particles themselves start to matter, and in compaction, grinding, wear and interlocking of angular grains, they are the whole story.
What PeriDEM does. It resolves deformation and fracture inside each particle while still handling particle-to-particle contact, so a grain can flatten at a contact, crack, and shed fragments that then participate in the assembly. Within a particle the model is a nonlocal continuum formulation, which accommodates cracks without tracking them; between particles it uses DEM-style contact laws applied at the discretization level. Neither half is novel on its own. Carrying both at once, for arbitrary particle shapes, is what lets the model show locking and particle-scale damage that rigid-particle DEM cannot represent.
What it costs, and what is being done about it. Resolving every grain is expensive, and it is not always needed: at any instant much of an assembly is not deforming, rearranging or breaking in a way that requires particle resolution. The current NSF-supported work is on multifidelity strategies: spending full particle-scale resolution only where deformation and breakage are actually happening, and a cheaper description everywhere else, while estimating the error introduced by replacing particle-resolved regions with a coarser description.
Grinding is where the rigid-particle assumption is least defensible: the whole point of the process is that particles wear and break. Here a container rotates with an internal protrusion, and circular, hexagonal, triangular and drum-shaped particles are carried up the wall and dropped through it. Contact force is what is colored, so the load path through the tumbling assembly is visible as it forms and releases, and each particle is a deformable, breakable solid, not a sphere with a contact law.
Magnetic soft composites are designed as if the particle–matrix interface were perfect. This project asks what changes when it is not, and whether that is what sets how long the material keeps working.
Effective properties for a composite have to come from somewhere. This project derives them from resolved micro-scale fracture simulations, after first settling which description of the interface to trust.
Well-posedness, kinetic relations and convergence rates for models of dynamic fracture, and the crack behavior they predict around voids, inclusions and interfaces.
Parallel and asynchronous solvers, load balancing and distributed data structures for large mechanics and transport problems.
