Logarithmic versus Andrade's transient creep: Role of elastic stress redistribution

Creep is defined as time-dependent deformation and rupture processes taking place within a material subjected to constant applied stress smaller than its athermal, time-independent strength. This time dependence is classically attributed to the thermal activation of local deformation events. The phenomenology of creep is characterized by several ubiquitous but empirical rheological and scaling laws. We focus here on primary creep following the onset of loading, for which a power law decay of the strain rate is observed, $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varepsilon}}\ensuremath{\sim}{t}^{\ensuremath{-}p}$, with the exponent $p$ varying between $\ensuremath{\simeq}0.4$ and 1, this upper bound defining the so-called logarithmic creep. Although this phenomenology is known for more than a century, the physical origin of Andrade-like $(p<1)$ creep remains unclear and debated. Here we show that $p<1$ values arise from the interplay between thermal activation and elastic stress redistribution. The latter stimulates creep dynamics from a shortening of waiting times between successive events, is associated to material damage and, possibly, at high temperature and/or stresses, gives rise to avalanches of deformation events.