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Speaker: Robert Lipton, Louisiana State University

Title: Nonlocal Dynamic Fracture

Abstract: The 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. In this talk a nonlocal fracture model is presented in which fractures emerge from the initial boundary value problem as part of the solution. The nonlocal model carries details of the process zone seen at the mesoscopic length scale. In the limit of vanishing nonlocality, solutions of the model converge to solutions of the wave equation with evolving boundary formulated in Dal Maso and Toader (J. Diff. Equ. 2019).  The classic kinetic relation linking crack velocity to elastic energy flux flowing into the crack tip is recovered in the limit of vanishing nonlocality. The nonlocal dynamic initial value problem implicitly encodes the features of the classic model and delivers them in the limit of vanishing nonlocality. The mesoscopic model eleminates the need for separate mathematical treatment of crack and intact material seen in classic (macroscopic) fracture models.

Biography: Robert Lipton works on the multi-scale analysis of heterogeneous media. Lipton's research includes the following areas: Identification of new wave phenomena due to sub-wavelength resonances and multiple scattering. Accurate multi-scale analysis of heterogeneous media with non well separated length scales. Non-local modeling for understanding the fracture process and the creation of interface. Chacterizing the macroscopic effect of the microstructure on strength. Identifying the macroscopic effect of microscopic interfaces. Extraction of the effect of microstructure on extreme elastic properties.