The importance of stress percolation patterns in rocks and other polycrystalline materials

Abstract

A new framework for thinking about the deformation behavior of rocks and other heterogeneous polycrystalline materials is proposed, based on understanding the patterns of stress transmission through these materials. Here, using finite element models, I show that stress percolates through polycrystalline materials that have heterogeneous elastic and plastic properties of the same order as those found in rocks. The pattern of stress percolation is related to the degree of heterogeneity in and statistical distribution of the elastic and plastic properties of the constituent grains in the aggregate. The development of these stress patterns leads directly to shear localization, and their existence provides insight into the formation of rhythmic features such as compositional banding and foliation in rocks that are reacting or dissolving while being deformed. In addition, this framework provides a foundation for understanding and predicting the macroscopic rheology of polycrystalline materials based on single-crystal elastic and plastic mechanical properties.

Measurement of Activation Volume for Creep of Dry Olivine at Upper‐Mantle Conditions

“…To the extent dislocation creep is active, its plastically anisotropic nature will cause load redistribution at the grain scale as grains favorably oriented for slip (“weak” orientations) yield and pass their load to grains at “hard” orientations (see, e.g., Merkel, ; Weidner et al, ). Elastic anisotropy can also contribute to grain‐scale load redistribution (Burnley, ). Given the geometry of detectors placed at different azimuths ψ (Figure ), in a sample with more or less random grain orientations, each detector must see diffracted photons from a different subpopulation of grains for any given ( hkl ) diffraction condition.…”

Network flow model of force transmission in unbonded and bonded granular media

“…Indeed, regardless of failure mode, diffused versus localized, the collective failure of force chains by buckling precipitates and controls global failure [12,14,17]. Detailed knowledge of the evolution of force chains and their confining weak neighbors, in 2D and 3D, is thus crucial for developing robust constitutive models that can adequately describe the deformation of many everyday granular materials (e.g., sand, rocks, ceramics, powders, and grains) [11,15,[18][19][20][21]. Although significant attention has been paid to force transmission in granular systems, little is known about the regulation of internal forces that leads to this dual pattern of heterogeneity, in particular, its dependence on the strength of the contacts as well as the local and global topology of the contact network of the material (e.g., Ref.…”

Thermodynamic equilibrium at heterogeneous pressure

“…It occurs in an assemblage with spinel, olivine, clinopyroxene, garnet and Fe-Ti oxides (mainly magnetite, ilmenite). The locality and rocks containing the Opx are described in detail by Vrijmoed et al (2006;2013). The Opx shows typically bowl-shaped zoning of Al 2 O 3 , where Al 2 O 3 content increases from core to rim.…”

“…Whereas viscous stresses relax over time, elastic stresses will always be there as long as there is an applied load. Burnley (2013) calculated the stress patterns resulting from purely elastic deformation, including plastic yielding, and discussed the implications of these patterns for metamorphic banding. Schrank et al (2012) investigate both experimentally and numerically the effects of thermal elasticity on stress distribution during heating of a granite.…”