The mechanics of anisotropic spring networks

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, $p_x$ and $p_y$, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of $p_x$ and $p_y$. 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.

References in corpus (14)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Criticality and isostaticity in fiber networks
• Force Chains, Microelasticity and Macroelasticity
• Green's Function Measurements of Force Transmission in 2D Granular Materials
• Stressed backbone and elasticity of random central-force systems
• Stiff Polymers, Foams and Fiber Networks
• Effective medium theory of semiflexible filamentous networks
• Anisotropy in granular media: classical elasticity and directed force chain network
• Soft modes and elasticity of nearly isostatic lattices: randomness and dissipation
• Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks
• Effective Medium Theory of Filamentous Triangular Lattice
• Rigidity percolation on the square lattice
• Local mechanical response in semiflexible polymer networks subjected to an axisymmetric prestress
• Orientational order and glassy states in networks of semiflexible polymers

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