Plate force due to bending at subduction zones

Bending of the lithosphere at subduction zones generates stresses that contribute to the force balance on plates. We determine the net horizontal force on subducting plates by imposing a simple kinematic description of strain in the equations that govern the mechanical equilibrium of a thin viscous sheet. The magnitude of the force depends on the velocity, thickness, and curvature of the subducting plate. Using representative values for old oceanic lithosphere, we obtain an effective horizontal force that is nearly 40% of the buoyancy force due to slabs in the upper mantle.