Modelling the large deformations in stratified media—the Cosserat continuum approach

Adhikary, Deepak; Mühlhaus, H. B.; Dyskin, Arcady

doi:10.1002/(sici)1099-1484(199905)4:3<195::aid-cfm59>3.0.co;2-#

Cited by 23 publications

(8 citation statements)

References 13 publications

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“…Continuum formulations based on anisotropic elasticity suffer from a change in character, from elliptic to hyperbolic; consequently projected results tend to be unrealistic (Hobbs et al 1976, p. 207). Even when Cosserat (couple-stress) continua are used to overcome such problems, the large rotations require a specialized, geometrically nonlinear treatment (Fleck et al 1995, Fleck 1997, Adhikary and Dyskin 1997, Adhikary and Dyskin 1998, Adhikary et al 1999. Even for the simplest mechanical models, perfect systems tend to exhibit infinite critical loads, with the corollary of extreme sensitivity to small disturbances or geometric misalignments.…”

Section: Kink Bands In Layered Structuresmentioning

confidence: 99%

The Maxwell stability criterion in pseudo-energy models of kink banding

Hunt

Peletier

Wadee

2000

Journal of Structural Geology

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Kink banding, common to many structures in nature and engineering, has several distinctive features-notably highly nonlinear snap-back instability leading to localization and sequential lock-up. The proposed friction model, although simplified, introduces these defining characteristics without obscuring them by including other effects of lesser immediate significance. In the absence of small imperfections or disturbances, linearized theory suggests that in its pre-kinked configuration the system never goes unstable. However, under sufficient applied end-displacement it is shown to be in a state of extreme metastability, such that micro-disturbances would trigger the nonlinear response. To overcome this problem we adopt an energy approach based on a global rather than a local stability criterion. When applied to imperfect systems with small initial misalignments, the critical displacement thus defined shows little of the sensitivity expected from other stability criteria, and provides a useful lower bound on the expected critical displacement and associated load. We offer the frictional model not as a complete description, but as a prototype to which other components can be added. Thus it provides information on the triggering, localization and lock-up processes, for example, but not on the choice of kink band width which is fixed a priori. Suggestions are provided throughout of extra energy contributions which will extend the model's capability.

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Section: Kink Bands In Layered Structuresmentioning

confidence: 99%

The Maxwell stability criterion in pseudo-energy models of kink banding

Hunt

Peletier

Wadee

2000

Journal of Structural Geology

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“…Adhikary and Dyskin (1997) successfully extended the application of the Cosserat theory into stratified rocks. The model was further developed to allow elastic-plastic slip occurring with no tension at the joints and large deformation analyses (Adhikary et al 1999(Adhikary et al , 2001). The developed model was incorporated into the finite element program COSFLOW (Chen et al 2002a, b;Guo et al 2003) and has been successfully applied to mining subsidence and water/gas flow analyses in layered rock (Guo 2004;Chen 2006).…”

Section: Numerical Simulation Of Layered Rocks and Cosserat Theorymentioning

confidence: 99%

Numerical Simulation of Bed Separation Development and Grout Injecting into Separations

Chen

Guo

2008

Geotech Geol Eng

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In this paper, the Cosserat theory that has been incorporated into a three dimensional finite element code COSFLOW, is applied to analyze the development of bed separations in the layered overburden and grout injection into the bed separations. The mechanism of bed separation development during the longwall mining is investigated. A parametric study is carried out to investigate the effect of major factors including hard rock grade, panel height and panel weight on bed separation development. Based on the modeling, a conceptual model to describe the development process of bed separation is proposed. The effect of grout injecting into the bed separations on subsidence reduction is also studied and the conclusion agrees well with the common realization.

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“…The "nite element formulation is described in detail in Adhikary et al [16]. For the veri"cation of the model, the critical self-weight for a package of vertical layers was computed and compared with the analytical solution.…”

Section: Numerical Verixcationmentioning

confidence: 99%

A numerical study of flexural buckling of foliated rock slopes

Adhikary

Mühlhaus

Dyskin

2001

Num Anal Meth Geomechanics

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SUMMARYThe occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic}perfectly plastic. Condition of slip at the interfaces are determined by a Mohr}Coulomb criterion with tension cut o! at zero normal stress. The theory is valid for large deformations. The model is incorporated into the "nite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against #exural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87}104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes.

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Modelling the large deformations in stratified media—the Cosserat continuum approach

Cited by 23 publications

References 13 publications

The Maxwell stability criterion in pseudo-energy models of kink banding

The Maxwell stability criterion in pseudo-energy models of kink banding

Numerical Simulation of Bed Separation Development and Grout Injecting into Separations

A numerical study of flexural buckling of foliated rock slopes

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