Overview: The peridynamic formulation is a
spatially nonlocal derivative free model for simulating problems of free crack
propagation.Material points interact through short-range forces and the
formulation allows for discontinuous deformations. Here the short-range forces
are initially elastic and soften beyond a critical relative displacement. We
upscale this peridynamic model to find the macroscopic (a.k.a. small horizon)
limit. It is shown that the limiting macroscopic evolution has bounded energy
given by the bulk and surface energies of brittle fracture mechanics. The
macroscopic evolution corresponds to the simultaneous evolution
of the fracture surface and linear elastic displacement away from the crack
set. The elastic moduli, wave speed, and energy release rate for the
macroscopic evolution are explicitly determined by moments of the peridynamic
potential energy. This provides an interesting new connection between nonlocal
short-range forces acting at the microscale to brittle fracture evolution at
the macroscale. This paper has appeared in the
Journal of Elasticity, January 3, 2014, and is available at:
https://www.math.lsu.edu/~lipton/SmallHorizonLimit-Peridynamics.pdf
http://link.springer.com/article/10.1007/s10659-013-9463-0/fulltext.html
