ORALS

An elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the “cosmic fabric” and spacetime with the fabric’s world volume. Using a Lagrangian formulation, we show that the fabric’s behavior as derived from Hooke’s Law is analogous to that of spacetime per the Field Equations of General Relativity (GR). The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric’s Lagrangian outside of inclusions is shown to have the same form as the Einstein–Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves and the energy density of free space. By introducing a mechanical analogy of GR, we enable the application of Solid Mechanics tools to address problems in Cosmology. Finally, because the cosmos acts as a continuum body with external tractions according to Cauchy’s Law, the existence of God is proven as exemplified by the tractions on the outside surface of the cosmos.

Simulations using a history-dependent and physically-motivated Internal State Variable (ISV) constitutive model implemented into a spherical Finite Element code, TERRA3D, for the entire Earth’s mantle is used to illustrate the catastrophic plate tectonics event in our Earth’s history. We investigate the kinetics of dynamic recrystallization, grain size, and their influences on the mantle dynamics during its convection. The unique aspect of this study was that an explicit recrystallization variable was introduced and connected with the grain size kinetics, thus unifying static (grain size increases) and dynamic recrystallization (grain size decreases). We found that significant dynamic recrystallization (grain size reduction) occurred in the descending slabs and adjacent mantle, thus weakening its strength. Due to the rheological weakening, frequent episodic overturns and mantle avalanches were observed. Furthermore, strongly heterogeneous microstructures and associated viscosities were predicted in the entire mantle, because of the competition between the dynamic recrystallization, grain refinement, and grain growth under the geological setting. The grain size tended to be larger (~106 µm) in the upper mantle (below the lithospheric mantle) as the grain growth rate overtook the grain size reduction rate, while relatively small grain sizes (102 ~ 103 µm) were observed in the lower mantle as dynamically recrystallized downwelling slabs continuously flowed. In particular, exceptional heterogeneity of microstructure and rheology was observed nearby the core-mantle boundary depending on the kinetics of the dynamic recrystallization and grain size. Amazingly, this high rate event appears to align with worldwide flood stories as documented in the bible as well as other ancient manuscripts such as the Epic of Gilgamesh.