GALCIT Colloquium

The study of deforming continuous media is a well developed branch of solid mechanics which typically relies on models that assume displacements within the media are sufficiently smooth such that they can be modeled with partial differential equations. However, observations of nature show that some displacements exist where the spatial partial derivatives cannot be evaluated, most notably at the tip of a moving crack. Simulations of crack propagation or other forms of material localization utilizing the common discretizations of these PDE's will typically produce results that are extremely mesh dependent. Generalized, nonlocal, continuum mechanics can be used as a replacement for the classical PDE's and can regularize numerical simulations of localization as well as include other physical features of heterogeneous materials such as wave dispersion. A generalized nonlocal continuum theory that has shown usefulness in the modeling material failure will be presented along with a recently developed nonlocal model for convection-diffusion. These two models have been coupled using an interacting continua approach. This seminar will introduce the audience to the coupled nonlocal theory, including a discussion of how non-locality at macroscales arises due to modeling decisions that exclude heterogeneity in microstructures and can lead to interesting phenomena such as characteristic length-scales in solid media and anomalous dispersion in fluid flow. Examples and large-scale simulations related to energy applications, specifically hydraulic fracturing, will be shown.