Quasi-Brittle Free Crack Propagation Using Cohesive Dynamics
Monday, May 11, 2015 - 3:35pm - 4:00pm
Geological formations comprised of oil shale are often quasi-brittle. Higher fidelity modeling beyond linear elastic fracture mechanics provides an opportunity to capture the effects of the process zone and softening near crack tips inside these materials. In this talk we present a non-local, nonlinear, cohesive continuum model of peridynamic type for assessing the deformation state inside a quasi-brittle formation. Here interaction forces between material points are initially elastic and then go unstable and soften beyond a critical relative displacement. The evolution inside the deforming body selects whether a material point lies inside or outside the process zone associated with nonlinear behavior. In this model the process zone geometry evolves with the applied load. This is in contrast to a classic cohesive zone fracture model that collapses the process zone onto predetermined fracture surfaces and assumes linear elastic deformation away from these surfaces. In this formulation the natural parameter that controls the size of the process zone is the ratio of the radius of the non-local interaction between material particles relative to the size of the deforming sample. An explicit inequality is identified showing how this relative length scale controls the volume of the process zone. The volume of the process zone is shown to vanish as the non-local interaction distance is decreased to zero. This formulation provides a family of parametrized models interpolating from quasi-brittle to brittle fracture evolution. To emphasize this aspect this we apply Gamma convergence arguments coming from the theory of image processing to discover that the limiting evolution has an energy density associated with a process zone that is confined to a surface. Distinguished limits of cohesive evolutions are identified and are found to have both bounded linear elastic energy and Griffith surface energy in the limit of vanishing non-locality.