Bending stress and dissipation in subducted lithosphere

Oceanic lithosphere undergoes permanent deformation during subduction once the stresses exceed the elastic limit. Departures from elastic behavior occur by brittle failure in the shallow lithosphere and by a combination of low‐ and high‐temperature creep at greater depths. We combine laboratory‐based rheological models with estimates of slab shape from earthquake hypocenters to quantify the bending stress and dissipation in subduction zones. The peak stress occurs at the depth of the brittle‐ductile transition, which is controlled mainly by lithospheric age. Integrals of the stress over the thickness of the plate are used to evaluate the resistive bending force and the bending moment. A representative value for the resistive force on old oceanic lithosphere is 3 × 10 12 N m −1 , which is comparable in magnitude to ridge push but opposite in direction. Both the bending force and moment are remarkably insensitive to the rate of subduction. In fact, the bending moment can be approximated using a simple power law rheology and a stress exponent of n ≈ 14. Such a large exponent implies that the lithosphere behaves like a perfectly plastic solid. For most subduction zones the bending moment saturates along the entire plate. As a consequence, the bending stress does not influence the development of curvature during subduction. This behavior may explain why the curvature of subducted lithosphere is nearly independent of age.