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