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Summary We use a hybrid boundary-integral/thin-sheet (‘BITS’) model to investigate the subduction of 2-D viscous sheets with composite diffusion creep/dislocation creep rheology, with a focus on the conditions required for slab necking and breakoff. To validate the model, we show that its predictions of the sinking speed of the slab follow a universal scaling law identical to one previously derived for purely Newtonian sheets. We obtain analytical expressions for the fiber stress resultant and bending moment of the sheet during deformation by pure stretching and pure bending, respectively, and show that the non-Newtonian dislocation creep component of the rheology significantly weakens the sheet for both types of deformation. We solve the BITS equations for two distinct situations: “free” subduction, in which the slab pulls an attached negatively buoyant plate without hindrance; and “arrested” subduction that slows or stops when a positively buoyant (continental) portion of the attached plate arrives at the trench. Strong lithospheric thinning is difficult to obtain in free subduction and requires dominantly non-Newtonian rheology, i.e. large (&gt;5) values of the characteristic ratio λ of the Newtonian to the non-Newtonian viscosity. However, during arrested subduction strong thinning leading to breakoff occurs for much lower values of λ, and the point of maximum thinning is at shallower depths. These results are explained by a one-dimensional viscous dripping model (‘DRIP’) of a vertical slab with a composite rheology and an arbitrary kinematically prescribed time-dependent convergence rate U0(t). By injecting into DRIP convergence histories predicted by BITS, we find that DRIP reproduces closely the results of the more complicated BITS model. The DRIP model shows that the convergence rate controls slab breakoff in two distinct ways. On the one hand, the rate of lithospheric thinning is proportional to the accumulated convergence, i.e., the time integral of U0(t). The breakoff depth, on the other hand, is controlled by the convergence rate history, being shallower when U0 rapidly decreases (arrested subduction) after an initial period of oceanic subduction.

Subduction of non-Newtonian plates: Thin-sheet dynamics of slab necking and breakoff