An elastoviscoplastic finite element model of lithospheric deformation

Via the finite element method, the stress state and deformation of the lithosphere were investigated with topographic loading. An elastoviscoplastic (EVP) rheology governed the mechanical response in a 40 km thick lithospheric plate of wet olivine. The viscous aspect of the rheology utilized a steady-state dislocation creep constitutive relation. The plastic part of the rheology treated frictional slip on faults within pervasively fractured rock via Byerlee's rule. The first studies use a time-invariant, steady-state conduction temperature distribution in the plate. These studies involved topographic loading with different maximum loads and different load growth rates. The EVP results were compared to elastic perfectly-plastic (EPP) solutions for plate bending as constrained by the Yield Strength Envelope (YSE) formulation for lithospheric mechanics. The EVP results included the often-overlooked effect that the load has on strengthening underlying rock against brittle deformation. The creep strain rate in the EVP models varied with time, depth, and lateral location, unlike the EPP/YSE models that constrain all creep to a single a priori creep strain rate. At the transition from frictional slip to creep, the EVP models showed a three km zone with contributions from both mechanisms, relative to the EPP/YSE's artificially sharp and immediate transition. The last study incorporated two variations on the temperature distribution in the EVP lithosphere. The "whole-lithosphere cooling model" cooled the plate during and after the load growth period, following the half-space cooling model for oceanic lithosphere. Unlike its non-cooling counterpart, the whole-lithosphere cooling model showed no further frictional slip after the load growth period. The "magma conduit model" used an initial temperature distribution that had a high temperature along a vertical symmetry axis during loading to approximate temperature effects from a magma conduit. After loading, its temperature distribution cooled with time to a steady-state distribution. The conduit model results lacked a deep normal faulting zone and showed a much different stress and strain distribution under the load. Both of these cooling models showed that the cooling of oceanic lithosphere caused its mechanical response at the end of loading to be "frozen in" over millions of years following the load growth period.