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

Abstract

AbstractTectonic 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.