Gradient Elastic Surfaces and the Elimination of Fracture Singularities in 3D Bodies

PDE Seminar
Tuesday, March 26, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Casey Rodriguez – University of North Carolina at Chapel Hill – crodrig@email.unc.edu
Gong Chen

In this talk, we give an overview of recent work in gradient elasticity.  We first give a friendly introduction to gradient elasticity—a mathematical framework for understanding three-dimensional bodies that do not dissipate a form of energy during deformation. Compared to classical elasticity theory, gradient elasticity incorporates higher spatial derivatives that encode certain microstructural information and become significant at small spatial scales. We then discuss a recently introduced theory of three-dimensional Green-elastic bodies containing gradient elastic material boundary surfaces. We then indicate how the resulting model successfully eliminates pathological singularities inherent in classical linear elastic fracture mechanics, presenting a new and geometric alternative theory of fracture.