scholarly journals A perturbative solution of the power-law viscoelastic constitutive equation for lithospheric rocks

1996 ◽  
Vol 39 (6) ◽  
Author(s):  
M. Dragoni ◽  
T. Lenci ◽  
S. Santini ◽  
F. Vetrano

A power-law, viscoelastic constitutive equation for lithospheric rocks, is considered. The equation is a nonlinear generalization of the Maxwell constitutive equation, in which the viscous deformation depends on the n-th power of deviatoric stress, and describes a medium which is elastic with respect to normal stress, but relaxes deviatoric stress. Power-law exponents equal to 2 and 3, which are most often found in laboratory experiments, are considered. The equation is solved by a perturbative method for a viscoelastic layer subjected to a constant, extensional or compressional, strain rate and yields stress as a function of time, temperature and rock composition. The solution is applied to an ideal extensional boundary zone and shows that the base of the crustal seismogenic layer may be deeper than predicted by a linear rheology.

Author(s):  
Aly El Domiaty ◽  
Abdel-Hamid I. Mourad ◽  
Abdel-Hakim Bouzid

One of the most significant approaches for predicting formability is the use of forming limit diagrams (FLDs). The development of the generalized model integrates other models. The first model is based on Von-Misses yield criterion (traditionally used for isotropic material) and power law constitutive equation considering the strain hardening exponent. The second model is also based on Von-Misses yield criterion but uses a power law constitutive equation that considers the effect of strain rate sensitivity factor. The third model is based on the modified Hill’s yield criterion (for anisotropic materials) and a power law constitutive equation that considers the strain hardening exponent. The current developed model is a generalized model which is formulated on the basis of the modified Hill yield criterion and a power law constitutive equation considering the effect of strain rate. A new controlling parameter (γ) for the limit strains was exploited. This parameter presents the rate of change of strain rate with respect to strain. As γ increases the level of the FLD raises indicating a better formability of the material.


1978 ◽  
Vol 45 (1) ◽  
pp. 111-113 ◽  
Author(s):  
A. Nachman ◽  
J. R. Walton

The problem of the sliding of a rigid asperity over a power law viscoelastic layer is examined in the realistic limit of infinite (dimensionless) layer thickness. For a contact interval of unit length, asymptotic expansions for the normal traction over the interval together with several other physically relevant quantities (e.g., the friction coefficient) are developed in terms of an appropriate asymptotic sequence of powers of the (dimensionless) layer thickness.


2017 ◽  
Vol 25 (03) ◽  
pp. 1750023 ◽  
Author(s):  
Nathalie Favretto-Cristini ◽  
Arkady M. Aizenberg ◽  
Bjørn Ursin ◽  
Paul Cristini ◽  
Anastasiya Tantsereva

The Discretized Kirchhoff Integral method has been recently tested against laboratory experiments using a model with surface curvatures and sharp edges generating wave diffraction effects. Comparisons between numerical and laboratory data have exhibited a good quantitative fit in terms of time arrivals and amplitudes, except in the vicinity of secondary shadow boundaries created by the interaction of the edges of some topographical structures. Following this work, the effect of multiple scattering and the surface curvatures on the wavefield is studied here, using the so-called diffraction attenuation coefficient, in order to define the cases where these effects may be neglected in the numerical modeling without loss of accuracy.


2007 ◽  
Vol 573 ◽  
pp. 339-369 ◽  
Author(s):  
M. G. WELLS ◽  
H. J. H. CLERCX ◽  
G. J. F. VAN HEIJST

Laboratory experiments and numerical simulations of oscillating spin-up in a square tank have been conducted to investigate the production of small-scale vorticity near the no-slip sidewalls of the container and the formation and subsequent decay of wall-generated quasi-two-dimensional vortices. The flow is made quasi-two-dimensional by a steady background rotation, and a small sinusoidal perturbation to the background rotation leads to the periodic formation of eddies in the corners of the tank by the roll-up of vorticity generated along the sidewalls. When the oscillation period is greater than the time scale required to advect a full-grown corner vortex to approximately halfway along the sidewall, dipole structures are observed to form. These dipoles migrate away from the walls, and the interior of the tank is continually filled with new vortices. The average size of these vortices appears to be largely controlled by the initial formation mechanism. Their vorticity decays from interactions with other stronger vortices that strip off filaments of vorticity, and by Ekman pumping at the bottom of the tank. Subsequent interactions between the weaker ‘old’ vortices and the ‘young’ vortices result in the straining, and finally the destruction, of older vortices. This inhibits the formation of large-scale vortices with diameters comparable to the size of the container.The laboratory experiments revealed a k−5/3 power law of the energy spectrum for small-to-intermediate wavenumbers. Measurements of the intensity spectrum of a passive scalar were consistent with the Batchelor prediction of a k−1 power law at large wavenumbers. Two-dimensional numerical simulations, under similar conditions to those in the experiments (with weak Ekman decay), were also performed and the simultaneous presence of a k−5/3 and k−3−ζ (with 0 < ζ « 1) power spectrum is observed, with the transition occurring at the wavenumber at which vorticity is injected from the viscous boundary layer into the interior. For higher Ekman decay rates, steeper spectra are obtained for the large wavenumber range, with ζ = O(1) and proportional to the Ekman decay rate. Movies are available with the online version of the paper.


Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 821-828 ◽  
Author(s):  
HANS J. HERRMANN ◽  
ALEXEI N.B. POLIAKOV ◽  
FRANK TZSCHICHHOLZ

When rocks are sheared very strongly they either fracture or flow plastically if the hydrostatic pressures are strong enough. Both cases have been studied extensively in geophysical examples and in laboratory experiments. The faults in the brittle case and the shear bands in the plastic case form fractal networks that reflect the detailed stress field and the history of the deformation. Origin of the fractal patterns are instabilities due to the non-linearity in the constitutive behavior. In both cases an internal fractal structure is also found: power-law distributed gouge in faults and multifractal strain rate distributions in shear bands. We show examples illustrating the important consequences of fractal concepts to the understanding of this field.


2021 ◽  
Author(s):  
João S. Rebelo ◽  
Célia P. F. Domingues ◽  
Francisca Monteiro ◽  
Teresa Nogueira ◽  
Francisco Dionisio

AbstractPersistence is a state of bacterial dormancy where cells with low metabolic activity and growth rates are phenotypically tolerant to antibiotics and other cytotoxic substances. Given its obvious advantage to bacteria, several researchers have been looking for the genetic mechanism behind persistence. However, other authors argue that there is no such mechanism and that persistence results from inadvertent cell errors. In this case, the persistent population should decay according to a power-law with a particular exponent of −2. Studying persisters’ decay is, therefore, a valuable way to understand persistence. Here we simulated the fate of susceptible cells in laboratory experiments in the context of indirect resistance. Eventually, under indirect resistance, detoxifying drug-resistant cells save the persister cells that leave the dormant state and resume growth. The simulations presented here show that, by assuming a power-law decline, the exponent is close to −2, which is the expected value if persistence results from unintentional errors. Whether persisters are cells in a moribund state or, on the contrary, result from a genetic program, should impact the research of anti-persistent drugs.Author SummaryPersistence, a form of bacterial dormancy, was discovered in the early days of the antibiotic era. Thanks to dormancy, these cells often evade antibiotic therapy and the immune system. However, despite its clinical importance, this phenotype’s nature is still under debate. Arguably, the prevailing view is that persistence is an evolved (selected for) bet-hedging mechanism to survive in the presence of cytotoxic agents such as antibiotics. In that case, the persister population should decay exponentially, although at a much slower pace than the non-persister population. A few authors recently advanced an alternative hypothesis: bacterial persistence results from many malfunctions and cell division errors. In this case, persistent populations should decay according to a power-law with exponent of −2, that is, according to 1/t2. Here we simulated the fate of susceptible bacterial cells in the presence of bactericidal antibiotics in the context of indirect resistance based on laboratory experiments performed earlier. By showing that the dynamics of persister cells is consistent with 1/t2, our results corroborate the hypothesis that the phenomenon of bacterial persistence is an accidental consequence of inadvertent cell problems and errors. If confirmed, this conclusion should impact the research strategies of anti-persistent drugs.“The following day, no one died. This fact, being absolutely contrary to life’s rules, provoked enormous and, in the circumstances, perfectly justifiable anxiety in people’s minds, for we have only to consider that in the entire forty volumes of universal history there is no mention, not even one exemplary case, of such a phenomenon ever having occurred…”Death with interruptionsJosé Saramago (2005)Nobel Prize for Literature 1998


2014 ◽  
Vol 2 (4) ◽  
pp. 2981-3013 ◽  
Author(s):  
S. M. Potirakis ◽  
K. Eftaxias ◽  
G. Balasis ◽  
J. Kopanas ◽  
G. Antonopoulos ◽  
...  

Abstract. Of particular interest is the detection of precursors of an impending rupture. Theoretical, numerical studies along with laboratory experiments indicate that precursory signs of an impending failure are the sudden drop of fractal dimension and entropy, along with the anticorrelated, for large system sizes, rising of Hurst exponent and drop of a frequency–size power-law scaling exponent. Based on the widely accepted concept of the self-affine nature of faulting and fracture, we examine whether these precursory signs exist in the fracto-electromagnetic emissions resulting from the activation of a single fault.


Sign in / Sign up

Export Citation Format

Share Document