Title: Nonlocality and length-scales in dynamic fracture: the peridynamic solution   

Speaker: Florin Bobaru, Associate Professor, University of Nebraska-Lincoln

Date/Time: Thursday, January 29, 2009, 2:00 PM

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Dynamic fracture is a complex phenomenon driven by what happens in a finite volume around the crack tip.  Under sufficiently fast loading conditions, a straight crack branches into two (and sometimes more) cracks that move along with speeds measured to be no more than 10% less than the speed measured just before branching.  Despite sustained efforts from the computational modeling and simulation community for the past few decades, the fundamental problem of dynamic crack branching in brittle materials has not had a satisfactory solution.  Existing solutions may show branching of the crack path, but the obtained crack propagation speeds do not resemble the experimentally measured values.  Difficulties with mesh dependency and lack of convergence are also noticed.  It has been recently argued that, in order to simulate dynamic fracture, multiscale models (coupling atomistic and continuum zones) may be needed.  However, the “process zone” in dynamic crack branching, for example, may be in the order of millimeters and the time scales in the order of microseconds.  These scales render a Multiscale approach where one scale is atomistic, even if possible, rather impractical, using the existing computational resources.  Nonlocal models are better able to eliminate mesh dependency and convergence problems in problems involving damage.  The new peridynamic method, a reformulation of classical continuum mechanics proposed by Silling in 2000, is used here to obtain the first correct prediction by computational simulation of the velocity profile and crack paths in dynamic crack branching of thin brittle plates.  I will also show how adaptive refinement can be developed for this nonlocal method and give an example of mixed-mode fracture (the Arrea-Ingraffea four-point blending problem).  The crack path in the four-point bending problem clearly shows the relation between material length-scale and the peridynamic horizon.  In peridynamics, cracks are not part of the problem; they are part of the solution.

CSRI POC: Stewart Silling (505) 844-3973