Applied Math Seminar- Nonlocal approaches to fracture in continuum and granular media

Title: Nonlocal approaches to fracture in continuum and granular media

Speaker: Debdeep Bhattachary, Department of Mathematics University of Utah

Abstract: Modeling and predicting the evolution of fracture in solids and granular material is of utmost importance in many biological, geophysical, and mechanical applications. Understanding how materials fail under various loading conditions can lead to sustainable design practices by reducing waste. A recent development in modeling deformations in continuum media is the use of nonlocal approaches, specifically peridynamics, which can accurately model the initiation and propagation of fractures as an emergent behavior. In this approach, the displacement field exhibits localized softening zones as jump sets associated with discontinuities in the solution.

In the first part of the talk, we demonstrate our PeriDEM method to study the effect of fracture, grain topology, and deformability in granular media. Coupling peridynamics with nonlocal analogs of contact forces used in the Discrete Element Method (DEM), we develop a massively parallel computational platform for high-fidelity simulations of large granular aggregates. We discuss several computational challenges associated with accommodating nonconvex particle shapes, self-contact between particle fragments, among others. We demonstrate the application of our model to several interdisciplinary problems including determining the bulk strength of brittle granular aggregates under uniaxial compression, vehicle mobility on dry gravel beds, the hopper flow problem, and the modeling of sea-ice floe dynamics.