Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed "hydrolytic weakening. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.
Bibliographical noteFunding Information:
We would like to acknowledge financial support from a wide range of international research organisations, notably: the Australian Predictive Mineral Discovery CRC (pmd * CRC), CSIRO Exploration and Mining, the Australian Computational Earth System Simulator (ACcESS) MNRF, the Swiss National Fund, the CSEDI, Math-GEO and ITR grants from the National Science Foundation as well as the Johannes Gutenberg-Universität Mainz. Sylvie Demouchy kindly supplied the diffusion profile shown in Figure 2.