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 $\Sigma$ 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.

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• Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
• Athermal creep deformation of ultrastable amorphous solids
• Soil creep facilitated by cyclic variations of environmental conditions