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Rigidity Loss in disordered systems; Three Scenarios

Disordered packings of soft particles and disordered collections of coupled springs are models for materials as diverse as foams, emulsions, sand and (bio)polymer networks. For all these, the network of contacts or connections governs their mechanics, and both classes of materials lose rigidity when the connectivity becomes too low. By comparing networks that are at the verge of failure, we uncover that packings exhibit a very strong response to the addition or removal of only one bond: every connection is crucial. Adding one bond leads to a rigid state where all bonds carry a load, and removing one bond leads to he complete fragmentation leading to many tiny patches connected by freely moving hinges. In random networks such dramatic response is completely absent, and even novel types of networks constructed to mimic packings fail to capture the unusual level of structural self-organization in sphere packings. These insights can contribute to improved designs of network materials: if every element optimally participates in bearing loads, one can maximize e.g. the strength-to-weight ratio. Physics
Publ. 02-04-2015 11:45
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