Mathematical analysis and convergent discretization of nonlinear fracture models, then PeriDEM, where deformable particles contact, fracture and fragment. That foundation now supports multiscale modeling of failure in heterogeneous materials.
When does particle-scale detail change the answer, and when will a coarser model do just as well? The NSF ERI project turns that question into adaptive multifidelity methods that concentrate resolution where fracture and failure demand it. In parallel, connecting microstructure and interfaces to effective elastic and fracture behavior in ceramic composites.
In a particle-reinforced composite a crack has options. It can run through the matrix, deflect or arrest at an interface, debond an inclusion, or split it, and each event redistributes stress and energy, changing which mechanism acts next.
The scientific question. How do matrix cracking, interface debonding, particle fracture and contact interactions compete to control strength, toughness, localization and residual load capacity in heterogeneous materials?
Granular materials are the complementary limit: breakage there also creates fragments, contacts and load paths, without a bonded matrix to carry them. The same descriptors of load redistribution and energy partition ought to transfer between the two, and testing whether they do is the point.
Underneath both sits a longer line of work on whether the models can be trusted at all. A simulation of a crack is only evidence if the formulation is well posed, if the discretization converges, and if the result is the material’s behavior rather than the mesh’s. Most of the published record in this thrust is exactly that: well-posedness for nonlinear models of dynamic fracture, a priori error estimates for finite-difference and finite-element discretizations, convergence rates in Hölder and Sobolev settings, kinetic relations recovered in the classical limit, and the solver engineering that makes any of it run at scale. It is unglamorous and it is the foundation: see mathematical foundations of fracture and scalable solvers. The particle-scale work above inherits its credibility from it.
PeriDEM and the NSF Engineering Research Initiation award on adaptive multifidelity modeling of heterogeneous materials provide the computational basis. The working hypothesis is that macroscopic failure is governed by the competition among matrix, interface and particle fracture, and that descriptors retaining that evolving redistribution predict failure better than an accumulated scalar damage law.
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.
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.
Particle-resolved and multifidelity modeling of granular assemblies whose particles deform, break and rearrange under load.
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.
