Abstract: A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. The existence and uniqueness of the displacement-failure set pair follow from the initial value problem. The displacement-failure pair satisfies energy balance. The length scale of nonlocality ε is taken to be small relative to the domain in Rd, d = 2, 3. The new nonlocal model delivers two-point strain dynamics on a subset of Rd × Rd. This dynamic provides energy that interpolates between volume energy corresponding to elastic behavior and surface energy corresponding to failure. The deformation energy resulting in material failure over a region R is given by a d − 1 dimensional integral that is uniformly bounded as ε →0. For fixed ε, this energy is nonzero for d − 1 dimensional regions R associated with flat crack surfaces. The failure energy is the Griffith fracture energy for a given crack R in terms of its area for d = 3 (or length for d = 2). Simulations illustrate fracture evolution through generation of an internal traction-free boundary as a wake left behind a moving strain concentration. Crack paths are seen to follow a maximal strain energy density criterion.
Speaker’s Bio: Dr. Robert Lipton is the Nicholson Professor of Mathematics at Louisiana State University. He is a Fellow of the Society of Industrial and Applied Mathematics, the American Mathematical Society, and the American Association for the Advancement of Science. Dr. Lipton is the Editor in Chief of SIAM Journal of Mathematical Analysis
Last Updated: February 13, 2024 - 1:59 pm