 | | 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
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 53, Issue 6 / 2018 | Next article >> |
| B.A. Zhukov, "Asymptotic Analysis of the Plane Strain State Generated by a Finite Longitudinal Shear Crack," Mech. Solids. 53 (6), 698-706 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
6 |
Pages |
698-706 |
| DOI |
10.3103/S0025654418060110 |
| Title |
Asymptotic Analysis of the Plane Strain State Generated by a Finite Longitudinal Shear Crack |
| Author(s) |
B.A. Zhukov (Volgograd State Technical University, pr. Lenina 28, Volgograd, 400131 Russia; Volgograd State SocioPedagogical University, pr. im. V.I. Lenina 27, Volgograd, 400066 Russia, zhukov.b.a@gmail.com) |
| Abstract |
In the linear theory of elasticity, an arbitrary crack is represented as a combination of three: longitudinal shear cracks, transverse shear cracks, and normal tear cracks that do not interact with each other. In the nonlinear theory, for some types of strain energy potentials, a finite longitudinal shear crack necessarily generates a strain in the transverse plane. This article proposes an asymptotic description of the deformed state of a crack in the transverse plane under the action of a finite longitudinal shear in an incompressible material with a Mooney-Rivlin potential, and an assessment is made of the effect of additional deformation on the condition of the start of a crack. |
| Keywords |
final deformations, hyperelasticity, incompressibility, longitudinal shift |
| References |
| 1. | D.A. Polignone and C.O. Horgan,
"Pure Torsion of Compressible Nonlinearly Elastic Circular Cylinders,"
Quart. Appl. Math. 49, 591-607 (1991). |
| 2. | R.L. Fosdick and B.G. Kao,
"Transverse Deformations Associated with Rectilinear Shear in Elastic Solids,"
J. Elast. 8 (2), 117-142 (1978). |
| 3. | F. Mollica and K.R. Rajagopal,
"Secondary Deformation due to Axial Shear of the Annular Region between Two Eccentrically Placed Cylinders,"
J. Elast. 48 (2), 103-123 (1997). |
| 4. | L.M. Zubov,
"On Reduction of Several Spatial Problems of Nonlinear Elasticity to Two-Dimensional Boundary-Value Problems,"
in Contemporary Problems of Continuum Mechanics. Proc. 5th Intern. Conf., Rostov-on-Don, 1999, Vol. 1 (Rostov Gos. Univ., NII Mekh. Prikl. Mat., Rostov-on-Don, 2000), pp. 83-87 [in Russian]. |
| 5. | B.A. Zhukov,
"Nonlinear Interaction of Finite Longitudinal Shear with Finite Torsion of a Rubber-Like Bushing,"
Izv. Akad. Nauk. Mekh. Tv. Tela,
No. 3, 127-135 (2015)
[Mech. Sol. (Engl. Transl.)
50 (3), 337-344 (2015)]. |
| 6. | R. de Pascalis, M. Destrade, and G. Saccomandi,
"The Stress Field in a Pulled Cork and Some Subtle Points in the Semi-Inverse Method of Nonlinear Elasticity,"
Proc. Roy. Soc. London
Ser. A. 463, 2945-2959 (2007). |
| 7. | M. Mooney,
"A Theory of Large Elastic Deformation,"
J. Appl. Phys. 11, 582 (1940). |
| 8. | G.P. Cherepanov,
Mechanics of Brittle Fracture
(Nauka, Moscow, 1974; McGraw-Hill, New York, 1979). |
| 9. | L.R.G. Treloar,
The Physics of Rubber Elasticity
(Oxford University Press, New York, 1949; Izd-vo AN SSSR, Moscow, 1953) [in Russian]. |
| 10. | C. Truesdell and W. Noll,
The Non-Linear Field Theories of Mechanics (Springer, N. Y., 2003). |
| 11. | B.A. Zhukov,
"A Modification of the Signorini Method for Plane Strains in an Incompressible Material,"
Izv. Akad. Nauk. Mekh. Tv. Tela,
No. 4, 59-67 (2001)
[Mech. Sol. (Engl. Transl.)
36 (4), 47-53 (2001)]. |
| 12. | K.F. Chernykh and Z.N. Litvinenkova,
Theory of Large Elastic Strains
(Izd-vo LGU, Leningrad, 1988) [in Russian]. |
| 13. | N.I. Muskhelishvili,
Some Basic Problems of Mathematical Theory of Elasticity
(Nauka, Moscow, 1966) [in Russian]. |
|
| Received |
24 March 2016 |
| Link to Fulltext |
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