Elastic-plastic flexure and heat flux on icy moons

Investigation of ice-shell flexure observed in elevation data is one of the few ways to infer the thermal evolution of icy moons. Most previous work have relied on the classical broken elastic plate model to infer the elastic thickness of the lithosphere, which was then converted to a heat flux using the equating bending moment approach or considering an analytical expression involving a Deborah number. Here, we compute more realistic elastic-plastic flexural profiles considering ice friction in the upper ice-shell and viscous flow at deeper levels. We show that the maximum curvature of the synthetic broken plate profile should be used when relating elastic thickness to heat flux and discuss that purely elastic models predict unrealistic oscillations near and in the flexural bulge region. We then discuss elastic thickness and heat flux relationships and provide a simple ad hoc analytical expression to relate both parameters.