Dynamics of plate bending at the trench and slab-plate coupling

The bending strength of subducting lithosphere plays a critical role in the Earth's plate tectonics and mantle convection, modulating the amount of slab pull transmitted to the surface and setting the boundary conditions under which plates move and deform. However, it is the subject of a lively debate how much of the potential energy of the downgoing plate is consumed in bending the plate and how the lithospheric strength is defined during this process. We model the subduction of a viscoelastic lithosphere, driven solely by the downgoing plate's buoyancy, freely sinking in a passive mantle, represented by drag forces. To investigate the dynamics of bending, (1) we vary the density and the viscosity profile within the plate from isoviscous, where strength is distributed, to strongly layered, where strength is concentrated in a thin core, and (2) we map the stress, strain, and dissipation along the downgoing plate. The effective plate strength during bending is not a simple function of average plate viscosity but is affected by rheological layering and plate thinning. Earth-like layered plates allow for the transmission of large fractions of slab pull (similar to 75-80%) through the bend and yield a net slab pull of F-SP(net) = 1 to 6 x 10(12) N m(-1), which varies with the buoyancy of plates. In all models, only a minor portion of the energy is dissipated in the bending. Surprisingly, bending dissipation hardly varies with lithospheric viscosity because in our dynamic system, the plates minimize overall dissipation rate by adjusting their bending curvature. As a result, bending dissipation, F B, is mainly controlled by the bending moment work rate exerted by slab pull. We propose a new analytical formulation that includes a viscosity-dependent bending radius, which allows for assessment of the relative bending dissipation in the Earth's subduction zones using parameters from a recent global compilation. This yields estimates of Phi(B)/Phi(TOT) < 20%. These results suggest that plates on Earth weakly resist bending, yet are able to propagate a large amount of slab pull.