Local shear stiffness switches between bending- and stretch-dominated regimes of a random net of elastic filaments

Abstract

Transitions in a random elastic network are investigated as a function of the stiffness of its constituents. As the local shear modulus, modelled as an energy cost of rotation among cross-linked filaments, is varied, we find a sharp transition between smaller and higher network shear stiffness, similar to that previously found for stretched networks. This transition is similar to the non-affine to affine transition observed in networks without local shear stiffness. We discover that, in the transition regime, the shear component of the total network stiffness shows a peak, and the stretch component increases until reaching a plateau, essentially causing the transition. With a suitable re-scaling of the measured network shear stiffness, we find a good collapse of the data on a single curve. Beyond the transition, in the very large combined bending and shear stiffness regime, we identify a marked stiffening of the network. We also investigate anisotropic networks to find that the transition to a stronger network becomes more emphasized, and the shear component of the total network shear modulus becomes higher during the transition. We suggest that networks, specially anisotropic ones, can be tuned between lower and higher overall shear stiffness by adjusting the local shear modulus using variable cross-linking components.