Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2017-5pp.541-548

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 52, Issue 5 / 2017 | Next article >>
N.A. Gorbushin and G.S. Mishuris, "Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice," Mech. Solids. 52 (5), 541-548 (2017)
Year 2017 Volume 52 Number 5 Pages 541-548
DOI 10.3103/S0025654417050090
Title Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice
Author(s) N.A. Gorbushin (Aberystwyth University, Penglais Campus, Penglais, Aberystwyth SY23 3FL, UK)
G.S. Mishuris (Aberystwyth University, Penglais Campus, Penglais, Aberystwyth SY23 3FL, UK, ggm@aber.ac.uk)
Abstract In this paper, the authors return to the classical problem of crack propagation in a lattice. The authors study the problems concerned with the possible regimes of stable steady-state crack propagation in an anisotropic lattice. They show that the steady-state crack propagation is impossible for some relations between the strength and elastic properties of the lattice. The authors also discuss the possibility of stable crack propagation at low speeds.
Keywords dynamic fracture of the lattice, stable crack propagation
References
1.  A. A. Griffith, "The Phenomena of Rupture and Flow in Solids," Philos. Trans. Roy. Soc. Ser. A 221, 163-198 (1921).
2.  J. D. Eshelby, "The Force on an Elastic Singularity," Philos. Trans. Roy. Soc. 244, 87-112 (1951).
3.  V. V. Novozhilov, "On a Necessary and Sufficient Criterion for Brittle Strength," Prikl. Mat. Mekh. 33 (2), 212-222 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (2), 201-210 (1969)].
4.  V. V. Novozhilov, "On the Foundations of a Theory of Equilibrium Cracks in Elastic Solids," Prikl. Mat. Mekh. 33 (5), 797-812 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (5), 777-790 (1969)].
5.  R. Thompson, C. Hsieh, and V. Rana, "Lattice Trapping of Fracture Cracks," J. Appl. Phys. 42 (8), 3154-3160 (1971).
6.  L. I. Slepyan, "Crack Propagation in High-frequency Lattice Vibration," Dokl. Akad. Nauk SSSR 260 (3), 566-569 (1981) [Sov. Phys. Dokl. (Engl. Transl.) 26, 900-902 (1981)].
7.  L. I. Slepyan, "On Discrete Models in Fracture Mechanics," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 46-59 (2010) [Mech. Solids (Engl. Transl.) 45 (6), 803-814 (2010)].
8.  L. I. Slepyan and L. V. Troyankina, "Fracture Wave in a Chain Structure," Zh. Prikl. Mekh. Tekhn. Fiz., No. 6, 128-134 (1984) [J. Appl. Mech. Phys. (Engl. Transl.) 25 (16), 921-927 (1984)].
9.  S. A. Kulakhmetova, V. A. Saraikin, and L. I. Slepyan, "Plane Problem of a Crack in a Lattice," Mech. Solids 19, 102-108 (1984).
10.  A. J. Rosakis, O. Samudrala, and D. Coker, "Cracks Faster then the Shear Wave Speed," Science 284 (5418), 1337-1340 (1999).
11.  H. Gao, Y. Huang, and F. F. Abraham, "Continuum and Atomic Studies of Intersonic Crack Propagation," J. Mech. Phys. Solids 49, 2113-2132 (2001).
12.  G. S. Mishuris, A. V. Movchan, and L. I. Slepyan, "Dynamics of a Bridged Crack in a Discrete Lattice," Quart. J. Mech. Appl. Math. 61 (2), 151-160 (2008).
13.  N. Gorbushin and G. Mishuris, "Analysis of Dynamic Failure of the Discrete Chain Structure with Nonlocal Interactions," Math. Mech. Appl. Sci., No. 23 (2016).
14.  G. S. Mishuris, A. V. Movchan, and L. I. Slepyan, "Localized Knife Waves in a Structured Interface," J. Mech. Phys. Solids 57, 1958-1979 (2009).
15.  L. I. Slepyan, Models and Phenomena in Fracture Mechanics (Springer, Berlin, 2002).
16.  L. Slepyan, A. Cherkaev, and E. Cherkaev, "Transition Waves in Bistable Structures. II. Analytical Solution: Wave Speed and Energy Dissipation," J. Mech. Phys. Solids 53 (2), 407-436 (2005).
17.  L. Truskinowsky and A. Vainchtein, "Kinetics of Martensite Phase Transitions: Lattice Model," SIAM J. Appl. Math. 66 (2), 533-553 (2005).
18.  J. Fineberg and M. Marder, "Instability in Dynamics Fracture," Phys. Rep. 313 (1), 1-108 (1999).
19.  L. Pechnik, H. Levinem, and D. A. Kessler, "Steady-State Mode I Cracks in a Viscoelastic Triangular Lattice," J. Mech. Phys. Solids 50 (3), 583-613 (2002).
20.  K. Ravi-Chandar, "Dynamic Fracture of Nominally Brittle Materials," Int. J. Fract. 90 (1), 83-102 (1998).
21.  J. R. Wills and A. V. Movchan, "Dynamic Weight Functions for a Moving Crack. I. Mode I Loading," J. Mech. Phys. Solids 43, 319-341 (1995).
22.  A. V. Movchan and J. R. Wills, "Dynamic Weight Functions for a Moving Crack. II. Shear Loading," J. Mech. Phys. Solids 43 (9), 1369-1383 (1995).
23.  A. Picclroaz, G. Mishuris, and A. V. Movchan, "Perturbation of Mode III Interfacial Cracks," Int. J. Fract. 166, 41-51 (2010).
24.  X. P. Xu and A. Needleman, "Numerical Simulations of Fast Crack Growth in Brittle Solids," J. Mech. Phys. Solids 42 (9), 1397-1434 (1994).
25.  M. Marder, "Simple Models of Rapid Fracture," Physica D 66, 125-134 (1993).
26.  L. I. Slepyan, A. B. Movchan, and G. S. Mishuris, "Crack in a Lattice Waveguide," Int. J. Fract. 162 (1-2), 91-106 (2010).
27.  L. I. Slepyan, M. V. Ayzenberg-Stepanenko, and G. Mishuris, "Forerunning Mode Transition in a Continuous Waveguide," J. Mech. Phys. Solids 78, 32-45 (2015).
28.  K. Ravi-Chandar, and W. G. Knauss, "An Experimental Investigation into Dynamic Fracture: III. On Steady-State Crack Propagation and Crack Branching," Int. J. Fract. 26, 141-154 (1984).
29.  M. Marder and S. Grass, "Origin of Crack Tip Instabilities," J. Mech. Phys. Solids 43 (1), 1-48 (1995).
30.  N. Gorbushin and G. Mishuris, "Dynamic Fracture of a Discrete Media under Moving Load," 2017.arXiv preprint arXiv:1701.02725.
31.  M. V. Ayzenberg-Stepanenko, G. Mishuris, and L. I. Slepyan, "Brittle Fracture in a Periodic Structure with Internal Potential Energy. Spontaneous Crack Propagation," Proc. Roy. Soc. London. Ser. A 470 (2167), 20140121 (2014).
32.  N. F. Morozov and M. V. Paukshto, Discrete and Hybrid Models of Fracture Mechanics (SPbGU, St. Petersburg, 1995) [in Russian].
33.  N. F. Morozov and M. V. Paukshto, "On the Crack Simulation and Solution in the Lattice," ASME J. Appl. Mech. 58, 290-292 (1991).
34.  N. Gorbushin and G. Mishuris, "On Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice," 2017.arXiv preprint arXiv:1701.04818.
Received 06 April 2017
Link to Fulltext
<< Previous article | Volume 52, Issue 5 / 2017 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100