On the theory of compressible, ideally plastic media

Ivlev, D. D.; Martynova, T. N.

doi:10.1016/0021-8928(63)90173-4

Cited by 6 publications

(8 citation statements)

References 2 publications

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“…The constant k is usually identified with the yield point, and the strain history parameters τ j are described by a kinetic equation, for example, in the form [9,10] Here ψ s > 0 for ∂f (s) ∂σ ijσ ij > 0 and ψ s = 0 for…”

Section: Introductionmentioning

confidence: 99%

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Conditions for the existence of discontinuity surfaces of irreversible strains in elastoplastic media

Буренин

Dudko

Семенов

2009

J Appl Mech Tech Phy

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Constraints are obtained on the stresses of a plastically compressed elastoplastic medium at which the occurrence of discontinuities of irreversible strains is possible. The loading surfaces are taken to be piecewise linear closed surfaces. Velocities of motion of irreversible-strain discontinuity surfaces are calculated.Introduction. Existence conditions and propagation mechanism of discontinuity surfaces of irreversible strains (dissipative shock waves) are necessary elements in the formulation of boundary-value problems of irreversible deformation dynamics and are a subject of continuous interest [1][2][3][4][5][6][7][8]. In model relations it is difficult to use rough loading surfaces with irreversible changes in volumetric strains taken into account. Strain discontinuities that arise in this case are combined, and the conditions for their occurrence differ greatly depending on what points of the loading surface correspond to prestress. The present paper considers piecewise linear loading surfaces.1. Basic Relations of the Model. Let the strains admitted by an elastoplastic medium be small, i.e., let the strain tensor components e ij be given by the relations

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Section: Introductionmentioning

confidence: 99%

“…We note that in [10], this parameter was taken to be the density of the medium, and in [9], it was volumetric strain.…”

Section: Introductionmentioning

confidence: 99%

Conditions for the existence of discontinuity surfaces of irreversible strains in elastoplastic media

Буренин

Dudko

Семенов

2009

J Appl Mech Tech Phy

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“…Equations ( Following [7], we will call the compressibility determined by Eq. (3) the "~ .... :L:~ced compressibility.…”

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“…For example, from thls law it follows that any deformation of a material Is accompanied by Its expansion. Depending on its initial density, ground may either undergo expansion or compaction during deformation [2].To eliminate this discrepancy between theory and experiment, some investigators [3,4] postulate expressions for the plastic potential which differ from the plasticity conditions and contain the experimentally determined coefficient of dilatancy.In thls case, however, the characteristics for the stresses and rates of deformation do not coincide, and therefore neither do the regions of the solutions for the stresses and deformations.Other methods for taking account of the compressibility of ground have been suggested [5,6], but in these too the characteristics for the stresses and rates of deformation do not coincide.We have developed a somewhat modified version of the method proposed by Ivlev and Martynova [7] for taking account of the compressibility of ground. We have obtained equ ations representing plane deformation of compressible ground, and have examined equations for fracture; an example illustrating the qualitative side of deformation of such ground is given.…”

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Plastic deformation of compressible ground

Zvonarev¹

1975

Soviet Mining Science

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To solve the problem of plastic flow of ground we usually enlist the associated f r law [i], i.e., it is assumed that the plastic potential exactly coincides with the cot • tlon of plasticity. The associated flow law enables us to solve a wlde range of problems, but In certain cases the theoretical results conflict with the actual data. For example, from thls law it follows that any deformation of a material Is accompanied by Its expansion. Depending on its initial density, ground may either undergo expansion or compaction during deformation [2].To eliminate this discrepancy between theory and experiment, some investigators [3,4] postulate expressions for the plastic potential which differ from the plasticity conditions and contain the experimentally determined coefficient of dilatancy.In thls case, however, the characteristics for the stresses and rates of deformation do not coincide, and therefore neither do the regions of the solutions for the stresses and deformations.Other methods for taking account of the compressibility of ground have been suggested [5,6], but in these too the characteristics for the stresses and rates of deformation do not coincide.We have developed a somewhat modified version of the method proposed by Ivlev and Martynova [7] for taking account of the compressibility of ground. We have obtained equ ations representing plane deformation of compressible ground, and have examined equations for fracture; an example illustrating the qualitative side of deformation of such ground is given.I. It will be assume that the following plasticity condition holds true for the ground: where 6ij is the Kronecker delta, and ~j the rates of deformation deviator components.From Eq. (2) we haveEquations (i), (3), and (4) show that e ~ 0 only when Ell # 0. If we put o = o, = ~,-a,-0, then Ia = Is = O, whence Ell = 0 and therefore e = 0. Thus the compressibility determined by Eq. (3) depends markedly on the distortion, and material for which Eq. (2) holds true cannot be compressed by hydrostatic pressure. Thls is observed only for overdense or completely waterlogged (outflow precluded) ground.All-Unlon Sclentlflc-Research Mlne Surveying Institute, Leningrad.

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