Scaling description of creep flow in amorphous solids

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 γ∼t^−ν, followed either by arrest or by a sudden fluidization. Various empirical laws have been suggested for the creep exponent ν and fluidization time τf in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between Σ and the transient yield stress Σt(γ) that characterizes the stability of configurations visited by the system at strain γ. Assuming the analyticity of Σt(γ) allows us to predict ν and asymptotic behaviors of τf in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.