Problem of plane strain of hardening and softening plastic materials

Ревуженко, А. Ф.; Shemyakin, E. I.

doi:10.1007/bf00851669

Cited by 12 publications

(11 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the local shear deformation along one side of a slip line can be expressed as 12 , r r only exist along the slip lines and describe the exact values of the shear deformation of elements along these lines. Apparently, the local deformation relates to the elements dimension.…”

Section: Shear Deformation Along Slip Linesmentioning

confidence: 99%

Elastoplastic model for discontinuous shear deformation of deep rock mass

Wang

Fan

et al. 2011

J. Cent. South Univ. Technol.

View full text Add to dashboard Cite

Deep rock mass possesses some unusual properties due to high earth stress, which further result in new problems that have not been well understood and explained up to date. In order to investigate the deformation mechanism, the complete deformation process of deep rock mass, with a great emphasis on local shear deformation stage, was analyzed in detail. The quasi continuous shear deformation of the deep rock mass is described by a combination of smooth functions: the averaged distribution of the original deformation field, and the local discontinuities along the slip lines. Hence, an elasto-plastic model is established for the shear deformation process, in which the rotational displacement is taken into account as well as the translational component. Numerical analysis method was developed for case study. Deformation process of a tunnel under high earth stress was investigated for verification.

show abstract

Section: Shear Deformation Along Slip Linesmentioning

confidence: 99%

Elastoplastic model for discontinuous shear deformation of deep rock mass

Wang

Fan

et al. 2011

J. Cent. South Univ. Technol.

View full text Add to dashboard Cite

show abstract

“…An estimate of the coefficients of structural weakening can be obtained with the approach developed by Revuzhenko and Shemyakin [10].…”

Section: On Rockmentioning

confidence: 99%

Mechanical characteristics of rock in place in analytical calculations on rock pressure phenomena in workings

Amusin¹

1979

Soviet Mining Science

View full text Add to dashboard Cite

ON ROCKIn the planning of main workings, the calculation of rock pressure manifestations in workings in an inhomogeneous stratified rock mass with fixed angles of dip (from flat-lying r steeply dipping) and with fixed angles between the axis of the working and the direction of the strike are of practical importance . The need to take account of the angle between the axis of the working and the direction of the strike leads to a threedimensional scheme of calculations. So far, the problem has not been solved over the whole of space with consideration of actual geometry and jointing of the rocks near the periphery of the working in time-dependent form by analytical or numerical methods. In planning work this problem is therefore solved by empirical methods; the data involve the strength of a rock fragment Rc and the depth of the working below the surface, which determines the stress state of the solid rock. The geological and mining conditions are taken into account by means of correction coefficients in the form of factors multiplying the calculated displacements and loads on the supports for typical conditions. This approach, which is based on a formal description of the results of field observations, which does not completely explain the mechanism of the phenomenon, and which takes no account of the variability in the rheology of rocks, is valid only in a limited range of conditions. To broaden this range and to improve the reliability of the predicted displacements and particularly of the load on the supports, it would be advantageous to make use of experimental-analytical methods. It would be rational to base them on analytical solutions for simple schemes of calculation (axial symmetry and homogeneous medium), but taking the fullest possible account of the theology and deformation properties of the medium; to correct the discrepancy between the assumed and actual schemes of calculation, it would be necessary to introduce empirical correction coefficients to the original data determining the state of stress and mechanical properties of the solid rock.Below we will discuss approaches to determination of the theoretical strengths and elastic and theological characteristics of the rocks, which can be used in analytical calculations on rock pressure phenomena in workings.Strength Characteristics. Analysis of the results of field tests on rock specimens of large size has established the relation between their strength and the number and direction of the system of fractures in relation to the direction of the greatest principal stress, the contact conditions at the fractures, the ratio of the dimensions of the specimens to those of the elementary rock blocks, and the relations between the elements of inhomogeneity in the specimens. The analogy between these relations and the above-mentioned features of the scheme of calculation resembling the real situation enables us to incorporate most of the correction coefficients into the calculated strength of the solid rock. Owing to the great difficulty of testing large rock...

show abstract

“…Further generalization to the class of hardening or weakening plastic materials reveals that the measure of shear on the slip area must have the dimensions of a length [2]. Thus, we must introduce parameters with the dimensions of a length, characterizing the discreteness of the network of sllp lines.Some of the equations of state take the form of relations between the stresses and the slips, with the dimensions of length; these are expressed in terms of the gradients of the displacements, a new kinematic variable, and the discreteness parameters of the network of sllp lines.Thus the continuous model [2] allows for the discreteness of the slip lines, and consequently occupies an intermediate position between the classical models of plasticity assuming infinitely close sllp lines and the fracture models in which the behavior of one or several essentially discrete cracks is considered (including shear cracks).If the stress--slip diagram has a descending branch, then the solution in terms of the equations in [2] can lead to the result that the sllp lines, along which load relief does not occur and the sllp increases, become essentially discrete.It is evident that such a transition to discrete lines is observed experimentally and is the cause of qualitatively new deformation effects [3,4].Thus, the equations of plasticity [2] lead to a model of the material with essentially discrete fracture surfaces on which tangential, and possibly normal, displacement discontinuities are associated with the stresses.This model borders on the class of models which are developed directly for cracks and in which account is taken of the interaction between their flanks [5][6][7][8].Let us consider some variational formulations of the boundary-value problems. (One of the possible variational approaches to problems of fracture was discussed in [9].)…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Variational formulation of some problems concerning fracture

Kramarenko¹,

Ревуженко²

1978

Soviet Mining Science

Self Cite

View full text Add to dashboard Cite

i. Problems concerning fracture are of great practical importance in mining and other branches of technology.The problem of fracture is closely associated with the general problem of plastic deformation of a continuous medium.We will consider an approach to fracture problems which follows from a successive development of one class of models of plasticity. We will limit ourselves to the case of plane deformation.In soil mechanics and rock mechanics we are faced with the problem of generalizing plasticity models for materials with internal friction.It is known that in plastic conditions, depending on the first invarlant of the stress tensor, the characteristics of the stress field are nonorthogonal.The construction of kinematic equations for such media leads to the necessity of introducing a new kinematic variable which represents the possible difference between the shears on the sllp areas from different families [i]. Further generalization to the class of hardening or weakening plastic materials reveals that the measure of shear on the slip area must have the dimensions of a length [2]. Thus, we must introduce parameters with the dimensions of a length, characterizing the discreteness of the network of sllp lines.Some of the equations of state take the form of relations between the stresses and the slips, with the dimensions of length; these are expressed in terms of the gradients of the displacements, a new kinematic variable, and the discreteness parameters of the network of sllp lines.Thus the continuous model [2] allows for the discreteness of the slip lines, and consequently occupies an intermediate position between the classical models of plasticity assuming infinitely close sllp lines and the fracture models in which the behavior of one or several essentially discrete cracks is considered (including shear cracks).If the stress--slip diagram has a descending branch, then the solution in terms of the equations in [2] can lead to the result that the sllp lines, along which load relief does not occur and the sllp increases, become essentially discrete.It is evident that such a transition to discrete lines is observed experimentally and is the cause of qualitatively new deformation effects [3,4].Thus, the equations of plasticity [2] lead to a model of the material with essentially discrete fracture surfaces on which tangential, and possibly normal, displacement discontinuities are associated with the stresses.This model borders on the class of models which are developed directly for cracks and in which account is taken of the interaction between their flanks [5][6][7][8].Let us consider some variational formulations of the boundary-value problems. (One of the possible variational approaches to problems of fracture was discussed in [9].) Let S denote the deformed region, bounded by the perimeter P. Let the region be divided by a line of possible discontinuity of the displacements L. Let us introduce Cartesian coordinates Ox~xa.The indices + and -will denote symbols pertaining to the regions to the right and left...

show abstract

Problem of plane strain of hardening and softening plastic materials

Cited by 12 publications

References 1 publication

Elastoplastic model for discontinuous shear deformation of deep rock mass

Elastoplastic model for discontinuous shear deformation of deep rock mass

Mechanical characteristics of rock in place in analytical calculations on rock pressure phenomena in workings

Variational formulation of some problems concerning fracture

Contact Info

Product

Resources

About