Skip to content..
Carnegie Mellon Center for Nonlinear Analysis
Peridynamics and Coarse Graining


Stewart A. Silling
Multiphysics Simulation Technologies Department
Sandia National Laboratories

: The peridynamic theory is an extension of traditional solid mechanics that treats discontinuous media, including the evolution of discontinuities due to fracture, on the same mathematical basis as classically smooth media. A recent advance in the linearized peridynamic theory permits the reduction of the number of degrees of freedom modeled within a body. Under equilibrium conditions, this coarse graining method exactly reproduces the internal forces on the coarsened degrees of freedom, including the effect of the omitted material that is no longer explicitly modeled. The method applies to heterogeneous as well as homogeneous media and accounts for defects in the material. The coarse graining procedure can be repeated over and over, resulting in a hierarchically coarsened description that, at each stage, continues to reproduce the exact internal forces present in the original, detailed model. Each coarsening step results in reduced computational cost.

This talk will cover the basics of the peridynamic theory. Then the new coarse graining method will be discussed, with computational examples. It will be demonstrated that the method produces accurate effective properties of a composite material.