Conditions for the localization of deformation in pressure-sensitive dilatant materials

Rudnicki, John W.; Rice, James R.

doi:10.1016/0022-5096(75)90001-0

Cited by 2,303 publications

(1,369 citation statements)

References 14 publications

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“…It has been shown by several researchers that for a wide class of elastoplastic models, at least one of the a 's is zero and therefore the search only needs to take place on the principal planes [38,[40][41][42]. For example, classical models such as von-Misses, Drucker-Prager, and Mohr-Coulomb can all be shown to localize within one of the principal planes, even for the case of finite strains, provided a suitable form of the elastic continuum tangent is utilized (isotropic).…”

Section: âmentioning

confidence: 99%

Capturing strain localization in dense sands with random density

Andrade

Borja

2006

Numerical Meth Engineering

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SUMMARYThis paper presents a three-invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density. A recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation. The new three-invariant constitutive model, similar to its two-invariant predecessor, is capable of accounting for meso-scale inhomogeneities as well as material and geometric nonlinearities. Details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed-form expression for the consistent tangent operator, whose spectral form is used in the strain localization analyses, is derived. An algorithm based on the spectral form of the so-called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop. The aforementioned framework is utilized in a series of boundary-value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso-scale and the intrinsic uncertainty associated with them.

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Section: âmentioning

confidence: 99%

Capturing strain localization in dense sands with random density

Andrade

Borja

2006

Numerical Meth Engineering

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“…Localized heterogeneities like fault zones control the development of the brittle upper crust (Ben-Zion and Sammis, 2013;Faulkner et al, 2010), whereas high temperature shear zones impose constraints on the mechanical behavior of the lower ductile crust (Bürgmann and Dresen, 2008;Handy et al, 2007;Platt and Behr, 2011;. Strain localization in the brittle regime may be described using damage rheology, continuum models or fracture mechanics-based approaches (Ashby and Sammis, 1990;Lyakhovsky and Ben Zion, 2014;Rudnicki and Rice, 1975). In the ductile field, localization may occur under varying thermodynamic boundary conditions and it may be associated with strain-dependent processes such as shear heating and melting, a change in the constitutive behavior by grain size reduction, enhanced water activity, or by the formation of a layered fabric in polyphase rocks (e.g., Montési, 2013;Getsinger et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Strain localization during high temperature creep of marble: The effect of inclusions

et al. 2014

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The deformation of rocks in the Earth's middle and lower crust is often localized in ductile shear zones. To better understand the initiation and propagation of high-temperature shear zones induced by the presence of structural and material heterogeneities, we performed deformation experiments in the dislocation creep regime on Carrara marble samples containing weak (limestone) or strong (novaculite) second phase inclusions. The samples were mostly deformed in torsion at a bulk shear strain rate of ≈ 1.9x10 -4 s -1 to bulk shear strains γ between 0.02 and 2.9 using a Paterson-type gas deformation apparatus at 900°C temperature and 400 MPa confining pressure. At low strain, twisted specimens with weak inclusions show minor strain hardening that is replaced by strain weakening at γ > 0.1 -0.2.Peak shear stress at the imposed conditions is about 20 MPa, which is ≈8% lower than the strength of intact samples. Strain progressively localized within the matrix with increasing bulk strain, but decayed rapidly with increasing distance from the inclusion tip.Microstructural analysis shows twinning and recrystallization within this process zone, with a strong crystallographic preferred orientation, dominated by {r} and (c) slip in .Recrystallization-induced weakening starts at local shear strain of about 1 in the process zone, corresponding to a bulk shear strain of about 0.1. In contrast, torsion of a sample containing strong inclusions deformed at similar stress as inclusion-free samples but do not show localization. The experiments demonstrate that the presence of weak heterogeneities initiates localized creep at local stress concentrations around the inclusion tips. Recrystallizationinduced grain size reduction may only locally promote grain boundary diffusion creep. Accordingly, the bulk strength of the twisted aggregate is close to or slightly below the lower (isostress) strength bound, determined from the flow strength and volume fraction of matrix and inclusions.

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“…This one-dimensionality assumption, implying the instantaneous CB formation over a large lateral extent, is justified by the above stated hypothesis of homogeneity of material and of stress state and was often used in the literature [e.g., Rudnicki and Rice, 1975].…”

Section: Dynamical Effects In the Cb Formationmentioning

confidence: 99%

“…Compaction localization was first predicted to occur by Rudnicki and Rice's [1975] strain localization theory, subsequently extended by Issen and Rudnicki [2000]. Among the main proposed collapse mechanisms are bond breakage [Nova et al, 2003], grain crushing [Mollema and Antonellini, 1996], pore collapse and pressure solution [Lajtai, 1974;Fletcher and Pollard, 1981;Olsson, 1999;De Meer et al, 2000].…”

Section: Introductionmentioning

confidence: 99%

Dynamical effects during compaction band formation affecting their spatial periodicity

Cecinato

Gajo

2014

JGR Solid Earth

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Compaction bands (CBs) are responsible for significant anisotropy alterations of permeability in geological materials; hence, understanding their formation conditions appears of key importance to all applications involving fluid extraction/injection from/into the ground. While most of the available models to understand CB formation are focused on interpreting the onset of a single CB, little effort has been so far dedicated to understand the documented periodicity of CBs. In this paper, the role of dynamical effects in inducing the post onset evolution of CBs is analyzed by means of a dedicated model for porous media with compressible constituents, with reference to a horizontal layer of sandy, water-saturated material. Elastic waves are generated as a first CB occurs due to sudden, localized volumetric collapse. If the waves are reflected at the interface with a softer material or with a previously formed CB, they produce significant local effective stress concentrations, which can promote the formation of further CBs in a cascade fashion, according to a regular geometric pattern. The spatial distribution of dynamically generated CBs, as well as the extent of the phenomenon, depends on the geometry of the domain and on the material's permeability. Sensitivity analysis is also performed to assess the key properties that promote dynamical CB in situ formation, identifying as the most influential conditions large stratum stiffness (increasing with depth) and the presence of softer layers. In contrast, the presence of less permeable and/or stiffer layers is not believed to play a major role in the proposed mechanism.

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Conditions for the localization of deformation in pressure-sensitive dilatant materials

Cited by 2,303 publications

References 14 publications

Capturing strain localization in dense sands with random density

Capturing strain localization in dense sands with random density

Strain localization during high temperature creep of marble: The effect of inclusions

Dynamical effects during compaction band formation affecting their spatial periodicity

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