Deformation localization in orogens: Spatiotemporal expression and thermodynamic constraint

Abstract

Orogens are spatiotemporal expressions of instabilities in materials under load, constrained by thermodynamics, and preserved in the cold outer shell of the planet. Their pressure–temperature–time histories are consistent with the predictions of differential grade-2 (DG-2) materials in pure shear. We place the statistically invariant shear localization mechanism of these materials in a coherent thermodynamic context using an analysis of strained elastic materials. This prototype system exhibits non-classical thermodynamic symmetry-breaking, where the potentials are all functions of a single variable and the distinction between heat and work fades from view. Consequently, internal energy must be described by a monotonically decreasing function of the entropy in order for heat capacity and absolute temperature to be positive. The entropy itself exhibits an inverse dependence on length. These constraints are satisfied by the overall shape and slope of the distributed deformation threshold ψD for DG-2 materials, and its noted 1/length correlation with naturally observed folds as a function of thermomechanical competence κ/χ. We predict that temperature in this non-linear elastic material will vary in proportion to the slope of ψD, being high at low competence, and low at high competence. Similar constraints apply to a self-gravitating body, where the energy function varies inversely with radius. Assigning zero pressure at the surface of the body, we also predict that pressure, the tensor trace of its stress–energy density, will vary inversely with radius. Thus, the body force of gravity will be expressed in this elastic self-gravitating system through the interplay of elastic and thermal lengths. Deformation localization in DG-2 materials arises due to the dynamic rescaling of lengths in response to a spike in the intrinsic energy ψI at κ/χ = ½. While the intrinsic ψI and localization ψL thresholds are monotonically decreasing for κ/χ > ½, they exhibit positive slopes at lower competence, signaling a return to classical thermodynamics and Joule heating in this transitional domain. Numerous structural and tectonic observations can be correlated using this remarkably simple model, beginning with the thickness and mechanical character of the brittle crust and oceanic lithosphere. In effect, this model projects the kinematic theory of plate tectonics into four-dimensional spacetime.