TY - JOUR

T1 - Mechanics of anisotropic spring networks

AU - Zhang, T.

AU - Schwarz, J. M.

AU - Das, Moumita

N1 - Publisher Copyright:
© 2014 American Physical Society.

PY - 2014/12/29

Y1 - 2014/12/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84920083939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920083939&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.90.062139

DO - 10.1103/PhysRevE.90.062139

M3 - Article

AN - SCOPUS:84920083939

SN - 1063-651X

VL - 90

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 6

M1 - 062139

ER -