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Rocks from the Earth mantle and polar ices have in common a nonlinear rheology and low crystal symmetries leading often to a limited number of independent slip systems for the glide or climb of dislocations. Both deform at elevated homologous temperatures, mostly under creep. Very large plastic deformation occurs during large scale geophysical flows, leading to pronounced crystallographic texture and an associated anisotropic rheology. Polar ice is a pure material, whereas several mineral phases are present simultaneously the mantle. The mantle deforms at extremely slow strain-rates, 10 orders of magnitude smaller than standard laboratory strain-rates, and thus the estimation of the mantle behaviour requires a drastic extrapolation from lab data. A consequence of the features outlined above is that deformation of mantle rocks or polar ices leads to a strong heterogeneity of the stress and strain-rate fields inside the polycrystalline aggregates, at the intragranular (micron) scale. This field heterogeneity has strong implication in terms of texture evolution, recrystallization, but also on the effective flow stress. Another consequence is that simple or ad-hoc micromechanical models are often inaccurate when the goal is to estimate the in situ nonlinear and anisotropic rheology, and the microstructure evolution at large strain, as the activation of slip systems is highly sensitive to stress fluctuations. In this presentation, we will review existing mean-field models for polycrystalline aggregates, show their capabilities / limitations with respect to reference full-field solutions, and show the benefit of the fully-optimized second order self-consistent scheme recently proposed by Song and Ponte Castaeda 2018. Examples for ice and few mantle minerals will be given for illustrative purpose. D. Song and P. Ponte Castaeda, Fully optimized second-order homogenization estimates for the macroscopic response and texture evolution of low-symmetry viscoplastic polycrystals, Int. J. plasticity 110 (2018), 272293
Castelnau et al. (Fri,) studied this question.