Mechanics of anisotropic spring networks

T. Zhang, J. M. Schwarz, Moumita Das

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We construct and analyze a model for a disordered linear spring network with anisotropy. The modeling is motivated by, for example, granular systems, nematic elastomers, and ultimately cytoskeletal networks exhibiting some underlying anisotropy. The model consists of a triangular lattice with two different bond occupation probabilities, px and py, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of px and py. We find that the onset of rigidity in the EMT agrees with Maxwell constraint counting. We also find beyond linear behavior in the shear and bulk modulus as a function of occupation probability in the rigid phase for small strains, which differs from the isotropic case. We compare our EMT with numerical simulations to find rather good agreement. Finally, we discuss the implications of extending the reach of effective medium theory as well as draw connections with prior work on both anisotropic and isotropic spring networks.

Original languageEnglish (US)
Article number062139
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number6
DOIs
StatePublished - Dec 29 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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