 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| I.A. Panteleev, D.V. Lozhkin, and V.A. Lyakhovsky, "Orientation of the Localized Damage Zone in Brittle Solid under True Triaxial Compression," Mech. Solids. 59 (5), 2776-2788 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
5 |
Pages |
2776-2788 |
| DOI |
10.1134/S0025654424604877 |
| Title |
Orientation of the Localized Damage Zone in Brittle Solid under True Triaxial Compression |
| Author(s) |
I.A. Panteleev (Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences, Perm, 614013 Russia, pia@icmm.ru)
D.V. Lozhkin (Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences, Perm, 614013 Russia, lozhkin.d@icmm.ru)
V.A. Lyakhovsky (Geological Survey of Israel, Jerusalem, Israel, vladimir.lyakhovsky@gmail.com) |
| Abstract |
The problem of finding the optimal orientation of the localized damage zone in a brittle material under triaxial compression with intermediate stress varying from the minimum (Karman scheme) to the maximum (Becker scheme) principal stress values is considered in the thin weak layer
approximation. The undamaged material is described by the relations of the linear-elastic isotropic body, the weak zone is described by the model of nonlinear elasticity of Academician of the Russian
Academy of Sciences V.P. Myasnikov with elastic moduli linearly dependent on the scalar parameter
of the damage. The orientation of the weakened zone is given by two angles relative to the direction of
action of the two principal stresses, and the degree of weakening is given by the value of the damage
parameter. The search for the optimal orientation of the zone for fixed values of the control parameters
consists in maximizing the function that determines the rate of damage growth in this zone.
As a result of the solution of the problem, the optimal orientations of the localized damage zone have
been established for different ratios of principal stresses and damage level. It is shown that with intermediate stress increase the angle of inclination of the zone relative to the direction of the maximum
principal stress decreases, as well as a narrowing of the interval of possible orientations of the zone relative to the direction of the intermediate principal stress. Based on the analysis of the ratio of the values
of the shear components of the stress tensor in the plane of the localized damage zone, the possible shear directions along this zone are determined. |
| Keywords |
true triaxial compression, damage localization zone, nonlinear elasticity, intermediate principal stress, orientation effects |
| Received |
30 July 2024 | Revised |
08 August 2024 | Accepted |
09 August 2024 |
| Link to Fulltext |
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