Scaling description of creep flow in amorphous solids

Abstract

Amorphous solids such as coffee foam, toothpaste or mayonnaise display a transient creep flow when a stress $Σ$ is suddenly imposed. The associated strain rate is commonly found to decay in time as $\dotγ \sim t^{-ν}$, followed either by arrest or by a sudden fluidisation. Various empirical laws have been suggested for the creep exponent $ν$ and fluidisation time $τ_f$ in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between $Σ$ and the transient yield stress $Σ_t(γ)$ that characterises the stability of configurations visited by the system at strain $γ$. Assuming the analyticity of $Σ_t(γ)$ allows us to predict $ν$ and asymptotic behaviours of $τ_f$ in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.