Dynamic Strain Localization in Fluid‐Saturated Porous Media

Loret, Benjamin; Prévost, Jean‐Hérve

doi:10.1061/(asce)0733-9399(1991)117:4(907)

Cited by 123 publications

(70 citation statements)

References 22 publications

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“…In the above theories the rate-independent nature of the material model is preserved. Incorporation of rate-dependent viscous terms can limit localization due to softening (Needleman, 1988;Loret and Prevost, 1990;Dubé et al, 1996). The size of the localization zone, however, is controlled by this rate effect and it may not be possible to fit, with the same expression of the evolution of damage or viscoplastic strains, the rate effect on the stress-strain response and a width of the localization zone that is consistent with experimental observations.…”

Section: Introductionsupporting

confidence: 70%

Bifurcation and creep effects in a viscoelastic non-local damageable continuum

Baxevanis¹,

Pijaudier‐Cabot²,

Dufour³

2008

European Journal of Mechanics - A/Solids

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To cite this version:Theocharis Baxevanis, Gilles Pijaudier-Cabot, Frédéric Dufour. Bifurcation and creep effects in a viscoelastic non-local damageable continuum. European Journal of Mechanics -A/Solids, Elsevier, 2009, 27 (4) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT AbstractThe conditions for localization in a material described by a non-local damage-based constitutive relation coupled with a Kelvin type creep relation are derived in a closed form. The inception of a localized mode is considered as a bifurcation into a harmonic mode. The criterion of bifurcation is reduced to the classical form of singularity of a pseudo acoustic tensor ; this tensor involves the elasto-damage strain and the total one at the inception of localization and the wavelength of the bifurcation mode through the Fourier transform of the weight function used in the definition of non-local damage. A geometrical approach was adopted to analyze localization for loading paths such that the elastic strain tensor is a fraction of the total strain tensor. Such loading paths include the general triaxial ones for which changes in the loading state occur only under time-independent processes (negligible creep strain during these changes of the stress state) and the uniaxial loading. The proposed coupled model preserves the properties of localization limiters; the minimum wavelength of the localization modes cannot be zero. The critical wavelength which is related to the width of the localization zone increases when the material parameter α (0 ≤ α ≤ 1), which is the fraction of creep strain entering into the evolution of damage, is decreasing. Under a certain condition on the growth of the loading function of damage and the initial state of deformation the critical wavelength decreases as the creep effect (creep strains) increases in accordance with experimental observations -increase of brittleness due to creep. In uniaxial tension, and for a

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Section: Introductionsupporting

confidence: 70%

Bifurcation and creep effects in a viscoelastic non-local damageable continuum

Baxevanis¹,

Pijaudier‐Cabot²,

Dufour³

2008

European Journal of Mechanics - A/Solids

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“…This is particularly problematic with constitutive equations modelling the degradation of the strength of materials as pressure of pore water may have an influence on shear band formation (Loret and Prevost 1991).…”

Section: Introductionmentioning

confidence: 99%

Modelling Hydromechanical Dilation Geomaterial—Cavitation and Localization

Sieffert

Buzzi

Collin

et al. 2014

Springer Series in Geomechanics and Geoengineering

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“…(1992) used local volume averaging technique in the derivation and argued that interaction torques caused by the skew-symmetrix portions should not be expected. Loret (1990) and, Loret and Pervost (1991) studied dynamic strain localization in saturated porous media. Boer et al (1993) formulated the field equations assuming both fluid and sohd constituents are incompressible and obtained an analytical solution for transient wave propagation.…”

Section: Application Of Mixture Theorymentioning

confidence: 99%

Chapter 5 Propagation of waves in porous media

Çorapçıoplu

Tuncay

1996

Advances in Porous Media

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Wave propagation in porous media is of interest in various diversified areas of science and engineer ing. The theory of the phenomenon has been studied extensively in soil mechanics, seismology, acoustics, earthquake engineering, ocean engineering, geophysics, and many other disciplines. This review presents a general survey of the Hterature within the context of porous media mechanics. Following a review of the Biot's theory of wave propagation in Unear, elastic, fluid saturated porous media which has been the basis of many analyses, we present various analytical and numerical solutions obtained by several researchers. Biot found that there are two dilatational waves and one rotational wave in a saturated porous medium. It has been noted that the second kind of dilatational wave is highly attenuated and is associated with a diffusion type process. The influence of couphng between two phases has a decreasing effect on the first kind wave and an increasing effect on the second wave. Procedures to predict the hquefaction of soils due to earthquakes have been reviewed in detail. Extension of Biot's theory to unsaturated soils has been discussed, and it was noted that, in general, equations developed for saturated media were employed for unsaturated media by replacing the density and compressibility terms with modified values for a water-air mixture. Various approaches to determine the permeabihty of porous media from attenuation of dilatational waves have been described in detail. Since the prediction of acoustic wave speeds and attenuations in marine sediments has been extensively studied in geophysics, these studies have been reviewed along with the studies on dissipation of water waves at ocean bottoms. The mixture theory which has been employed by various researchers in continuum mechanics is also discussed within the context of this review. Then, we present an alternative approach to obtain governing equations of wave propagation in porous media from macro scopic balance equations. Finally, we present an analysis of wave propagation in fractured porous media saturated by two immiscible fluids.

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Dynamic Strain Localization in Fluid‐Saturated Porous Media

Cited by 123 publications

References 22 publications

Bifurcation and creep effects in a viscoelastic non-local damageable continuum

Bifurcation and creep effects in a viscoelastic non-local damageable continuum

Modelling Hydromechanical Dilation Geomaterial—Cavitation and Localization

Chapter 5 Propagation of waves in porous media

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