Past Event: Babuška Forum

Nonlocal models for complex fracture simulations

Robert Lipton, Professor, Mathematics Department, Louisiana State Universitiy

Abstract

The dynamic fracture of brittle solids is a particularly interesting collective interaction connecting both large and small length scales. Apply enough stress or strain to a sample of brittle material and one eventually snaps bonds at the atomistic scale leading to fracture of the macroscopic specimen. We discuss a nonlocal model for computational dynamic fracture. In this lecture we apply simple methods of calculus to validate the nonlocal model by comparing its energy to the classic brittle fracture energy introduced by Griffith in 1920. Away from the crack set the time evolution of the nonlocal model is shown to be close to that of classic linear elastodynamics. Judicious rules of thumb are found for selecting the length scale of nonlocality based on dynamic stability. These rules are found also using straight forward and familiar calculus methods. Bio: Robert Lipton holds an S.B. Barton Professorship in the LSU Mathematics Department. He received his B.S. in Electrical Engineering from the University of Colorado in 1981 and his Ph.D. in Mathematics from the Courant Institute in 1986. He is a Fellow of the AAAS. He has authored over 90 papers in Applied Mathematics, Engineering, and Applied Physics. His research is funded by AFOSR, ARO and NSF.