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

粘性和弹性板的弯曲是一个很好理解的问题，具有广泛的工程和物理应用。粘弹性板的弯曲，特别是在3-D中，以及如果另外粘度随应力和/或温度非线性地变化，则不太好地表征。在这个项目中，我们将研究这种板在重力端力作用下和浸入粘性流体中的弯曲。在项目的第一部分中，我们将研究粘弹性弯曲，使用有限元软件包Abaqus对板进行建模，并结合边界元方法来捕获周围流体的阻力。在第二部分中，我们将研究粘性板的弯曲与非线性（应力和温度相关）流变学，使用代码流体开发的AMCG组在ESE部门，它具有自适应网格划分能力。我们将运行一套系统的不同宽度，粘度对比，杨氏模量和非线性粘度参数以及有和没有内部密度对比的板模型。最后，我们将应用我们的见解来研究地球构造板块的俯冲过程。以前已经表明，弯曲的能量学对俯冲过程和控制板块速度、板块耦合以及随之而来的地表变形（造山或海盆张开）和地震发生的可能性施加了至关重要的控制。

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.