13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 6. CONCLUSIONS The energy approach is used to propose a model of arising of regular systems of cracks, emerging the surface of a circular cavity, being observed, for example, around oil and gas wells under uniform compression. The cracks are supposed to arise due to the accumulation of elastic compression energy in the system. The limit compression (the exhaustion of strength) being achieved, a network of cracks is formed in the most stressed layer adjacent to the interior of the body, thus utilizing the accumulated elastic energy of this layer. In this case, of all the possible grids the least energy-consuming one is formed, that is, the system with such a number n and length L of the cracks, that the energy needed for its creation is minimal. In the simplest scheme the number n of "petals"-wedges arising from the cracking turns out to be equal to 5 (which corresponds to 2n = 10 cracks) and (contrary to limit compression pressure magnitude) be independent on geometrical and physical-mechanical parameters of the problem. The approach presented can be obviously formalized in the form of a corresponding variational principle of E.M. Morozov type [5, p. 11-24], provided that the core of the functional there introduced, would be modified appropriately and will be proportional not to the maximum normal stress or the maximum linear strain (similar to the first and second strength theories [5, p. 12]), but to the value, corresponding to the failure criterion here adopted. Acknowledgements The author is grateful to N.M. Osipenko for useful and stimulating discussions, and A.O. Chernyavsky for literary references and interesting indications. This work was partially supported by the Russian Foundation for Basic Research (grant № 11-08-01243-a). References 1. V.I.Karev, The influence of the stress-strain state of the rocks to the filtration process, and well production. Dr. Sc. Thesis, SPb., 2010 [in Russian]. 2. Y.F. Kovalenko, Geomechanics of oil and gas wells. Dr. Sc. Thesis, M., 2012 [in Russian]. 3. A.O. Cherniavsky, Crack grids in structures and natural objects, Mashinostroenie, M, 2010 [in Russian]. 4. J. Walker, Cracks in a Surface / / Sci. Amer. - 1986. - Vol. 255, N4. - P. 158-164. 5. A.V. Dumansky A.Y. Ishlinskii On the patterns of tree bark cracking Dokl. USSR Academy of Sciences, 1952, Vol 84, № 1, p. 161-164 [in Russian]. 6. S.S. Solntsev, E.M. Morozov, Glass fracture. Mashinostroenie, M, 1978 [in Russian]. 8. R.V. Goldstein, Compression failure / / Adv. in Mech, 2003. Vol. 2. Number 2. P. 3-20 [in Russian]. 7. R.V. Goldstein, N.M. Osipenko, Modeling delamination of coatings under thermomechanical loading in beam approximation / / Mechanics of Solids. 2007. Number 5. Pp. 75-90. 9. V.E. Panin, S.V. Panin., R.V. Goldstein, Mesomechanics of multiple cracking of brittle coatings in a loaded solid, International Journal of Fracture. 2008. Vol. 150. № 1-2. Pp. 37-53. 10. R.V. Goldstein, N.M. Osipenko, The gradual development of the fracture structure in the neighborhood of a longitudinal shear crack front. DAN. 2012. Vol. 445. Number 2. Pp. 164-167.
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