3D bending of complex rheology plates and applications to plate tectonics

Viscous and elastic plate bending are well-understood problems with a wide range of engineering and physical applications. Less well characterised is the bending of visco-elastic plates, in particular in 3-D and if additionally the viscosities vary non-linearly with stress and/or temperature. In this project, we will study the bending of such plates under a gravitational end force and immersed in a viscous fluid. In the first part of the project, we will investigate visco-elastic bending, using the finite-element package Abaqus to model the plates, coupled with a boundary element method to capture the resistance of the surrounding fluid. In the second part, we will study the bending of viscous plates with a non-linear (stress and temperature-dependent) rheology, using the code Fluidity developed in the AMCG group in the ESE department, which has adaptive meshing capabilities. We will run a systematic set of models of plates of different widths, viscosity contrasts, Young's moduli and non-linear viscosity parameters as well as with and without internal density contrasts. Finally, we will apply our insights to study the process of subduction of the Earth's tectonic plates. It has been previously shown that the energetics of bending exert a crucial control on the subduction process and control plate velocities, plate coupling and the consequent styles of surface deformation (mountain building or ocean basin opening) and the potential for the generation of earthquakes.