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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 solid-like contact), or expands (this represents a broken contact). Our goal is to study distribution of solid-like contacts in the energy-minimizing configuration. We prove that under certain geometric conditions on the network, there are at least two non-stretched springs attached to each node, which means that every particle has at least two solid-like contacts. The result implies that a particle cannot loose contact with all of its neighbors. This eliminates micro-avalanches as a mechanism for structural weakening in small shear deformation.
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