Peridynamics, Scaling, and Dynamic Fracture in Brittle Materials
Robert Lipton (LSU)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium B
Tue 4:20 - 5:40
CIT 227
Peridynamics, proposed by Stewart Silling in 2000, is a nonlocal formulation of continuum mechanics capable of simulating defects and cracks all the while expressed in terms of smooth potentials and free of spatial derivatives. We consider peridynamic formulations with bonds that soften beyond a critical stretch. Distinguished scaling limits are identified for this class of state based peridynamic models. The scaling limit of the peridynamic flow corresponds to an evolution expressed in terms of elastic displacement fields satisfying the wave equation away from crack paths inside cracking brittle materials. The limit evolutions satisfy energy balance expressed in terms of the usual kinetic energy of the motion together with an effective linear elastic energy and a Griffiths surface energy localized to the crack set. The elastic moduli and energy release rate are expressed explicitly in terms of moments of the peridynamic influence function, and parameters associated with the peridynamic potential energy.