Nonlinear flexure and equivalent mechanical thickness of the lithosphere

The elastic flexural thickness of the lithosphere depends on plate curvature. As curvature increases, the elastic core of the plate is thinned from above (frictional yielding) and from below (plastic creep). Sometimes decoupling between crust and mantle elastic cores can also occur. The mechanical thickness of the lithosphere, on the other hand, is the thickness of the rheologically layered plate having a strength above a critical threshold. In order to estimate the mechanical thickness from a simple uniform-rheology plate model, we adopt a plastic work-hardening constitutive equation, which results in lower stresses in the regions of high strain, relative to the elastic model. It is, therefore, a better approximation to the actual rheology of the flexed lithosphere where there is no lower-crustal decoupling (e.g., in oceanic and in cold continental lithosphere). The equivalent mechanical thickness of the nonlinear plate can be directly obtained, if the curvature is known, from the estimated elastic flexural rigidity or thickness. Comparison with numerical integration of bending moment in rheologically layered lithosphere shows that equivalent mechanical thickness is a good estimation of mechanical thickness. Examination of both oceanic and continental data suggests that mechanical thickness is controlled by the 900 ± 100°C isotherm. This corresponds to a creep strength of the order of 10 MPa in upper mantle material.