On the development of a theory of ideal plasticity

Ivlev, D. D.

doi:10.1016/0021-8928(58)90050-9

Cited by 13 publications

(11 citation statements)

References 1 publication

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“…Each of the ~blj values (j ~< 4) admitted on the average 6 variants, and the ~b2j values were chosen so that ~b21 = ~b22; ~b23 =/3, ~b24 = ~b25. Considering condition (13) with respect to ~b2j values, only one cycle was organized with four possible variants. As has been shown by preliminary and more accurate calculations, this basically rough division for variables kj and ~bij may cause an error in the determination of a not exceeding 0.5 percent.…”

Section: Computation Resultsmentioning

confidence: 99%

“…It is necessary to justify the possibility to extend this solution to the remaining part of the body [13].…”

Section: Modelling Of the Limit Regionmentioning

confidence: 99%

“…In addition, function ¢(qo) is not quite arbitrary either. Apart from satisfying condition (13), it should be such that everywhere within S the combination of Nx, N~o and L is statically admissible.…”

Section: [M~] H = H(x)as(t2/4)mentioning

confidence: 99%

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The ultimate ductile state model for a pipe with an axial through crack

Оrynyak

Torop

1996

Int J Fract

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A statistically admissible solution has been constructed for a pipe with an axial through crack. The boundaries of the limit region have been obtained and the strength conditions on its boundary have been formulated. The extension of the distribution of forces and moments beyond the limit region boundary has been substantiated. The results obtained for a pipe with closed ends are in fair agreement with the experimental data. The influence of the axial force and the property anisotropy upon the fracture stress has been studied. The possibility of considering several cracks is analysed.

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Section: Computation Resultsmentioning

confidence: 99%

“…It is necessary to justify the possibility to extend this solution to the remaining part of the body [13].…”

Section: Modelling Of the Limit Regionmentioning

confidence: 99%

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The ultimate ductile state model for a pipe with an axial through crack

Оrynyak

Torop

1996

Int J Fract

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“…The idea for this model is similar to the model (105 [96]. The rotationally symmetric model of von Mises is presented for comparison…”

Section: Triquadratic Modelmentioning

confidence: 99%

Phenomenological Yield and Failure Criteria

Altenbach

Bolchoun

Kolupaev

2013

Plasticity of Pressure-Sensitive Materials

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Models for isotropic materials based on the equivalent stress concept are discussed. At first, so-called classical models which are useful in the case of absolutely brittle or ideal ductile materials are presented. Tests for basic stress states are suggested. At second, standard models describing the intermediate range between the absolutely brittle and ideal-ductile behavior are introduced. Any criterion is expressed by various mathematical equations formulated, for example, in terms of invariants. At the same time the criteria can be visualized which simplifies the application. At third, in the main part pressure-insensitive, pressure-sensitive and combined models are separated. Fitting methods based on mathematical, physical and geometrical criteria are necessary. Finally, three examples (gray cast iron, poly(oxymethylene) (POM) and poly(vinyl chloride) (PVC) hard foam) demonstrates the application of different approaches in modeling certain limit behavior. Two appendices are necessary for a better understanding of this chapter: in Chap. 2 applied invariants are briefly introduced and a table of discussed in this chapter criteria with references is given.

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“…On these assumptions, the system of as follows equation of equilibrium 0,.~ +__ (2) where k and ~ are the cohesion and the angle of internal friction of the rock, and g is the plastic potential.…”

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confidence: 99%

Calculating rock displacement using the mechanics for a continuous medium

Zvonarev¹

1970

Soviet Mining Science

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The problem of determining the parameters of displacement of solid rock" can be formulated as follows. In a heavy half-plane we have a cut AD (Fig. 1) which becomes filled under gravity with the material of the half-plane. We consider the density and strength characteristics of this material to be known, together with the distribution of the velocity vector v or the displacement vector u along the contour of the cut. From these data we are to determine the displacements and stresses throughout the solid rock affected by the displacement. We shall be satisfied with determinations of the mean displacements and stresses; i.e., we assume that the displacements and stresses are continuous and differentiable with respect ~o the coordinates and to time over the whole region, except perhaps for isolated lines and points. This assumption enables us to solve the problem of displacement using the equations of mechanics for a continuous medium-the equation of motion, the equation of strength (for which we use the equation expressing the Coulomb strength law), and the equation relating deformation velocity to stress (the equation of the associated-flow law).We will introduce some simplifying assumptions: we will consider only the plane case; we assume that the displacement process occurs so slowly that the influence of time can be neglected; the only bulk force is to be that of gravity; and we assume that the density is constant over the whole region.On these assumptions, the system of as follows equation of equilibrium 0,.~ +__ Ox equations representing the displacement process in the solid rock wiI1 be O'txY --O, O~xy + O:y --T;(1) OyOx dy Coulomb equation f = (~ -%)2 + 4,~ ,y --sin ,~ (% -q-% + 2k ctg .~)* = 0; equation for the associated-flow law [1, 2] ex=)" Og. ~y=), Og. ), Og O ~x O ~y ~'xy 0 ~xy (2) where k and ~ are the cohesion and the angle of internal friction of the rock, and g is the plastic potential. If, as usual [1, 2],we use a function ff for the plastic potential and bear in mind [3] the relation % / = ~ (1 _+ sin ~ cos 20) --H, %y = n sin ~ sin 20, (3) ~y l where o = (o x + Oy + 2H)/2, H = 2k cot q0, and 0 is the angle between o I and the x axis, then for the components of the deformation velocity vector we get All-Union Scientific-Research Mine Surveying Institute (VNIMI), Leningrad. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp.

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On the development of a theory of ideal plasticity

Cited by 13 publications

References 1 publication

The ultimate ductile state model for a pipe with an axial through crack

The ultimate ductile state model for a pipe with an axial through crack

Phenomenological Yield and Failure Criteria

Calculating rock displacement using the mechanics for a continuous medium

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