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Homogenization and correctors for the wave equation in non periodic perforated domains
A network model of geometrically constrained deformations of granular materials
1.  Department of Mathematics, Washington State University, Pullman, WA 99164, United States, United States 
2.  Department of Mathematics and Materials Research Institute, Penn State University, University Park, PA 16802 
When the network deforms, each spring either preserves its length (this corresponds to a solidlike contact), or expands (this represents a broken contact). Our goal is to study distribution of solidlike contacts in the energyminimizing configuration. We prove that under certain geometric conditions on the network, there are at least two nonstretched springs attached to each node, which means that every particle has at least two solidlike contacts. The result implies that a particle cannot loose contact with all of its neighbors. This eliminates microavalanches as a mechanism for structural weakening in small shear deformation.
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