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Abstract Quartz is an abundant mineral in Earth's crust whose mechanical behavior plays a significant role in the deformation of the continental lithosphere. However, the viscoplastic rheology of quartz is difficult to measure experimentally at low temperatures without high confining pressures due to the tendency of quartz (and other geologic materials) to fracture under these conditions. Instrumented nanoindentation experiments inhibit cracking even at ambient conditions, by imposing locally high mean stress, allowing for the measurement of the viscoplastic rheology of hard materials over a wide range of temperatures. Here we measure the indentation hardness of four synthetic quartz specimens and one natural quartz specimen with varying water contents over a temperature range of 23°C to 500°C. Yield stress, which is calculated from hardness but is model dependent, is fit to a constitutive flow law for low‐temperature plasticity to estimate the athermal Peierls stress of quartz. Below 500°C, the yield stresses presented here are lower than those obtained by extrapolating a flow law constrained by experiments at higher temperatures irrespective of the applied model. Indentation hardness and yield stress depend weakly on crystallographic orientation but show no dependence on water content.
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Advanced Newton Methods for Geodynamical Models of Stokes Flow With Viscoplastic Rheologies
Abstract Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress‐velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity‐pressure form. To study different solution algorithms, we implement 2‐D and 3‐D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed‐point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.
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- PAR ID:
- 10453922
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geochemistry, Geophysics, Geosystems
- Volume:
- 21
- Issue:
- 9
- ISSN:
- 1525-2027
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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