Universal properties of creep flow in amorphous solids

Amorphous solids, such as atomic glasses, colloidal suspensions, granular matter or foams, begin to deform plastically when exposed to external stress Σ. Steady state deformation rate ∂_tε of these materials in absence of thermal fluctuations is usually described as ∂_tε ∼ (Σ − Σ_c)^β for stresses above critical stress Σ_c and vanishes below it, while in presence of thermal fluctuations flow persists below Σ_c, but is exponentially suppressed. The transient plastic deformation rate, called creep flow, is much less understood despite its importance in practical applications. Creep flow often displays a power-law decay in time ∂_tε ∼ t^−μ after which it can either arrest or eventually yield at fluidisation time τ_f. In recent years various numerical values and/or laws have been suggested for the exponent μ and time τ_f in particular experimental or numerical studies. We propose that mechanism underlying creep flow is the same as that of the steady state flow, which allows us to predicts parameters μ and τ_f of creep flow in terms of the steady state flow parameters, both in athermal and thermally activated systems. We successfully tested all our predictions using different mesoscopic elasto-plastic models of amorphous solids and found them to be consistent with published experimental results.