Journal Article

Flexure with damage

David M. Manaker, Donald L. Turcotte and Louise H. Kellogg

in Geophysical Journal International

Volume 166, issue 3, pages 1368-1383
Published in print September 2006 | ISSN: 0956-540X
Published online September 2006 | e-ISSN: 1365-246X | DOI:

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Ductile behaviour in rocks is often associated with plasticity due to dislocation motion or diffusion under high pressures and temperatures. However, ductile behaviour can also occur in brittle materials. An example would be cataclastic flow associated with folding at shallow crustal levels. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. In this paper we utilize a modified form of damage mechanics that includes a yield stress. Here, damage represents a reduction in frictional strength. We use this empirical approach to simulate bending of the lithosphere through the problem of plate flexure.

We use numerical simulations to obtain quasi-static solutions to the Navier equations of elasticity. We use the program GeoFEST v. 4.5 (Geophysical Finite Element Simulation Tool), developed by NASA Jet Propulsion Laboratory, to generate solutions for each time step. When the von Mises stress exceeds the critical stress on an element we apply damage to reduce the shear modulus of the element. Damage is calculated at each time step by a power-law relationship of the ratio of the critical stress to the von Mises stress and the critical strain to the von Mises strain. This results in the relaxation of the material due to increasing damage. To test our method, we apply our damage rheology to a semi-infinite plate deforming under its own weight. Where the von Mises stress exceeds the critical stress, we simulate the formation of damage and observe the time-dependent relaxation of the stress and strain to near the yield strength. We simulate a wide range of behaviours from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Using this method, stress relaxation produces perfectly plastic behaviour in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage, analogous to the acceleration of microcrack formation and acoustic emissions prior to failure. Thus continuum damage mechanics can be used to simulate the irreversible deformation of brittle materials.

Keywords: crustal deformation; flexure of the lithosphere; geodynamics; rheology; shear modulus

Journal Article.  9073 words.  Illustrated.

Subjects: Geophysics