Reversible viscoelasticity and irreversible elastoplasticity in the power law creep and yielding of gels and fibre network materials under stress

TL;DR

This study computationally investigates the creep and yielding behavior of fibre networks under stress, revealing viscoelastic and elastoplastic regimes, the impact of network connectivity, and conditions leading to material failure.

Contribution

It introduces a minimal model capturing viscoelastic and elastoplastic responses in fibre networks, highlighting the role of network connectivity and damage accumulation in creep and failure.

Findings

Power law creep observed at marginal connectivity (Z=4) with strain rate t^{-1/2}.

Irreversible filament breakage leads to elastoplastic creep and potential catastrophic failure.

Viscoelastic recovery depends on the balance between reversible and irreversible deformation.

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 irreversible 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 damage 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.