Shear localization in solids: insights for mountain building processes from a frame-indifferent ideal material model

Abstract

Tectonic and orogenic processes, reflecting the dynamic nature of the planet, provide myriad examples of the failure of Earth materials under load. Despite this wealth of data, the shear localization process remains a difficult physical modelling problem, lying at the frontiers of complex and non-linear systems research. We present a non-conventional continuum-physics approach to address this problem, based on the mathematical properties of differential grade-2 (DG-2) materials. We choose this material because it is both frame-indifferent, and general enough to include other, simpler materials as special cases. DG-2 materials in pure shear exhibit a dynamic rescaling mechanism, associated with localized shearing, which links the spatial and temporal scales of this process in a self-consistent manner, independent of the observer. On typical thermal timescales, the thermomechanical competence of DG-2 materials depends on the ratio of thermal to mechanical diffusivities, κ/χ. On this basis, we hypothesize the effective rigidity of Earth materials, pertaining when the thermomechanical competence is greater than unity. This theory, applied to the whole Earth, suggests the existence of isopycnal ‘detachment’ zones at systematic, globally correlated depths beneath orogens, consistent with a variety of geological data.

On the dynamics and thermodynamics of terrestrial planets

“…Note that vorticity terms are retained, consistent with the documented dynamic connection between normal stress differences and vorticity [5]. Therefore residual terms proportional to β 1 can drive toroidal motions.…”

“…Based on the work of Dunn & Rajagopal [11] it is expected that normal stress effects proportional to β 1 and β 2 will be of the same order of magnitude. The former is associated with finite material strength [5,17,18], and the latter with attenuation [19].…”

“…Note that σ kk denotes the sum of these components, consistent with the summation convention. Combining (5) with the hydrostatic relation p = ρgz, where g is gravitational acceleration and z is depth beneath the surface of the planet, we obtain…”

“…From a distant perspective this makes sense given that all planets, even the terrestrial ones, are spheroidally shaped. The viscosity of Earth's mantle, estimated based on observations of post-glacial isostatic rebound, is generally agreed to be strongly temperature dependent and huge, something like 10 21 P a − s. Of course, this does not mean that geodynamicists actually believe Earth's radial gravity-topography admittance (red) and correlation (blue) spectra (after [4]), compared with hypothetical wavebands for lateral strength and density heterogeneities, based on ThERM [5]. Horizontal gray bars span from 2 to ζ times the depths to lithospheric L1 − 4 and mantle M 1 − 4 modes of that model.…”

A nonlinear and time‐dependent visco‐elasto‐plastic rheology model for studying shock‐physics phenomena

“…develop and improve numerical rheology models to further increase the realism of numerical simulations.It is widely known that the viscous rheologic properties of the mantle material have a significant effect on tectonic processes, such as subduction, folding [e.g. Hobbs et al, 2007], mountain formation [Patton and Watkinson, 2010] and even the growth of fractures and faults [Nguyen et al, 2013]. It has been also established that extremely large meteorite impacts could have induced significant deformation of the Earth's mantle during the Hadean era of heavy meteorite bombardment […”