Viscoelasticity and elastoplasticity in the power law creep and yielding of gels and fibre network materials under stress

Abstract

We study computationally the creep and yielding of athermal gels and fibre network materials under a constant imposed shear stress, within a minimal model of interconnected filaments with central forces in $d=2$ spatial dimensions. Each filament is assumed Hookean initially, then breaks irreversibly above a threshold strain. At early times after the imposition of a small stress, we find purely viscoelastic creep response associated with non-affine deformations within the material, with solid terminal behaviour for a network coordination $Z>2d=4$ and initially floppy response for $Z<4$. For a marginally connected network, $Z=4$, we find sustained power law creep with a strain rate $\dot{\gamma}\sim t^{-1/2}$ and strain $\gamma \sim t^{1/2}$ as a function of time $t$ after the imposition of the stress. This viscoelastic regime gives way at later times to elastoplastic creep arising from filament breakage, broadening the range of values of $Z$ and time over which power law creep occurs, compared to a network with filament breakage disallowed. This accumulating filament breakage can weaken the network to such an extent that catastrophic material failure then occurs after a long delay, which we characterise. Finally, we consider the implications of viscoelastic versus elastoplastic deformation for the extent to which a material will recover its original shape if the load is removed after some interval of creep.