Nonlinear behavior of stochastic athermal fiber networks with elastic–plastic fibers

Abstract

Stochastic fiber networks form the structural component of network materials, which are broadly encountered in engineering and biology. Apparent elastic–plastic behavior, characterized by a yield point and softening at larger strains, is observed in some of these materials. A range of mechanisms, some of which being unrelated to fiber plasticity, may cause this behavior. In this work we investigate network plasticity caused by the plastic deformation of fibers and develop a comprehensive perspective on its relationship with network structural parameters. We determine the scaling of the yield stress and yield strain with network parameters emphasizing differences between the affine and non-affine deformation regimes. The non-linear response of the network is more complex when fiber plasticity takes place than in the purely elastic case. We describe four non-linear regimes and their dependence on network parameters. Further, we evaluate the dissipation and residual strains resulting upon loading–unloading cycles for a variety of networks and discuss design strategies for maximizing energy dissipation. Finally, we provide guidelines for the interpretation of experimental results and discuss ways to distinguish between various mechanisms that may cause a yield point and apparent elastic–plastic behavior.