The role of elasticity in slab bending

Previous studies showed that plate rheology exerts a dominant control on the shape and velocity of subducting plates. Here, we perform a systematic investigation of the role of elasticity in slab bending, using fully dynamic 2‐D models where an elastic, viscoelastic, or viscoelastoplastic plate subducts freely into a purely viscous mantle. We derive a scaling relationship between the bending radius of viscoelastic slabs and the Deborah number, De , which is the ratio of Maxwell time over deformation time. We show that De controls the ratio of elastically stored energy over viscously dissipated energy and find that at D e > 10 − 2, substantially less energy is required to bend a viscoelastic slab to the same shape as a purely viscous slab with the same intrinsic viscosity. Elastically stored energy at higher De favors retreating modes of subduction via unbending, while trench advance only occurs for some cases with D e < 10 − 2. We estimate the apparent Deborah numbers of natural subduction zones and find values ranging from10 − 3to > 1, where most zones have low D e < 10 − 2, but a few young plates have De  > 0.1. Slabs with D e < 10 − 2either have very low viscosities or they may be yielding, in which case our De estimates may be underestimated by up to an order of magnitude, potentially pointing towards a significant role of elasticity in ∼ 60 % of the subduction zones. In support of such a role of elasticity in subduction, we find that increasing De correlates with increasing proportion of larger seismic events in both instrumental and historic catalogues.