A test of the validity of yield strength envelopes with an elastoviscoplastic finite element model

Abstract

We have generated an elastoviscoplastic (EVP) rheological model of the lithosphere with an extended Maxwell model containing (in series) a linear elastic component, a creep component based on a flow law for dislocation creep in olivine, and a frictional component simulating Drucker-Prager plasticity based on Byerlee's rule. Finite element analyses for topographic loading of this oceanic lithosphere were carried out with two separate final loads (100 and 150 MPa) that were reached by four different load growth times (0, 0.1, 1, 10 Myr). Our results for the stress state and deformation of loaded lithosphere at 41.7 Myr into the model run are compared to results generated by the mechanical response of a time-independent elastic-perfectly plastic (EP) lithosphere, using a moment-curvature relationship based on the constant strain-rate yield strength envelope (YSE) and adopting a strain-rate representative of the EVP solution at 41.7 Myr. With identical flexural loading and material parameters, the deflection profiles of the EVP and EP solutions are quite similar, but it is unclear how the EP strain rate could be selected a priori without guidance from the EVP solution. For example, this uncertainty translates to about a 5 per cent error per decade of strain rate in the temperature gradient obtained by matching maximum moment and curvature in our EP models. The stress distributions of the time-dependent EVP model show deviations from the EP model (as defined by the YSE and an elastic core) in crystal plastic (macroscopically continuous dislocation creep) regions, where we observe vertical, lateral and temporal variations in the strain rate. At times much greater than the load growth time, the stress distribution in the lithosphere is independent of the loading rate and depends on the load magnitude only in that portion of the lithosphere that yields to frictional slip. After loading ceases, residual creep zones develop (in the vicinity of the brittle-plastic transition and the elastic-creep transition), driven by high stress in these regions.

Dynamics of retreating slabs: 1. Insights from two‐dimensional numerical experiments

“…Results from laboratory experiments of olivine rheology [ Kohlstedt et al , 1995] confirm this finding and additionally indicate that the Maxwell time is not constant but decreases with increasing strain rate; this produces a shear thinning flow, which is well known in fluid dynamics [ Karagiannis et al , 1988]. This result prompted the development of alternative, solid mechanical approaches, that use idealized nonlinear rheologies such as elastoplastic [ Chery et al , 1991] and full nonlinear elastoviscoplastic formulations [ Regenauer‐Lieb and Yuen , 1998; Albert et al , 2000; Branlund et al , 2001]. Elastoplastic failure of the lithosphere at trenches has been postulated to explain the trench profile in the Aleutians, Kuriles, Mariana, and Tonga regions.…”

Efficient early global relaxation of asteroid Vesta

“…Failure occurs in cells where the most compressive principal stress σ 1 exceeds 5σ 3 where σ 3 is the least compressive principal stress. A self-consistent viscoplastic solution requires that the stress tensor does not imply further brittle failure anywhere in the solution domain (Albert et al, 2000). We im-plement plasticity using an iterative approach whereby the effective viscosity of each cell that experiences brittle failure is lowered after each iteration of the finite element flow model until no cells experience further failure (e.g., Kaus (2010); King and Hager (1990)).…”

Why intracontinental basins subside longer: 3‐D feedback effects of lithospheric cooling and sedimentation on the flexural strength of the lithosphere

“…Therefore, our rheological model likely overestimates the long-term lithospheric strength. This behavior could be in principle modulated by accounting for viscous softening within the ductile domain of the plate [Albert et al, 2006;Huismans and Beaumont, 2011], though there are some concerns on the physical derivation of usually adopted weakening laws [Regenauer-Lieb et al, 2006]. Therefore, lithospheric strength as calculated by our approach should be considered as representing an upper bound.…”