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The viscoplastic behavior of polycrystalline Mg$_2$SiO$_4$ wadsleyiteaggregates, a major high pressure phase of the mantle transition zone of theEarth (depth range: 410 -- 520 km), is obtained by properly bridging severalscale transition models. At the very fine nanometric scale corresponding to thedisloca-tion core structure, the behavior of thermally activated plastic slipis modeled for strain-rates relevant for laboratory experimental conditions, athigh pressure and for a wide range of temperatures, based on thePeierls-Nabarro-Galerkin model. Corresponding single slip reference resolvedshear stresses and associated constitutive equations are deduced from Orowan'sequation in order to describe the average viscoplastic behavior at the grainscale, for the easiest slip systems. These data have been implemented in twograin-polycrystal scale transition models, a mean-field one (the recentFully-Optimized Second-Order Viscoplastic Self-Consistent scheme of [44])allowing rapid evaluation of the effective viscosity of polycrystallineaggregates , and a full-field (FFT based [45] [33]) method allowinginvestigating stress and strain-rate localization in typical microstructuresand heterogeneous activation of slip systems within grains. Calculations havebeen performed at pressure and temperatures relevant for in-situ conditions.Results are in very good agreement with available mechanical tests conducted atstrain-rates typical for laboratory experiments.

Multiscale modeling of the effective viscoplastic behavior of Mg$_2$SiO$_4$ wadsleyite: Bridging atomic and polycrystal scales