A technique for incorporating geothermal gradients and nonlinear creep into lithospheric flexure models

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Abstract
A beam flexure model for the lithosphere, which employs a nonlinear viscous creep constitutive relation, has been developed for time‐dependent flexure caused by surficial loads. The lithosphere is buoyantly supported by the underlying asthenosphere, which is modeled as an elastic (Winkler) foundation. Creep is highly dependent on temperature and melting point, which in turn vary with depth; these factors are incorporated into the beam lithospheric model by using Weertman's constitutive relation for creep of rock at elevated temperature. A typical value of the creep powernin the Weertman equation is 3 for rock, but the value ofnmay be varied in the model. The governing nonlinear partial differential equations for moment and deflection are solved by an analytical procedure for the spatial coordinate and by a numerical marching procedure in the time coordinate. Stresses in the lithosphere are also evaluated, with special attention given to an iterative technique for locating the neutral axis, which will not be at the centroid because of the nonlinearity and the geothermal gradient.