Abstract
This paper proposes a method to solve problems for interface tunnel defects in a piecewise-homogeneous elastic material that is under generalized plane strain and has no planes of elastic symmetry. The method is based on integral relations between the discontinuities and sums of the components of the displacement vector and stress tensor at the interface. Closed-form solutions are obtained for a system of interface tunnel inclusions with mixed contact conditions between the space and the inclusions. The dependences of the indices of singularity of the solutions on orthogonal coordinate transformation are established for different combinations of materials of monoclinic and orthorhombic systems. The effect of the antiplane component on the behavior of the solutions is revealed
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. S. Aleksandrov and T. V. Ryzhova, “Elastic properties of crystals (review),” Kristallografiya, 6, No. 2, 289–314 (1961).
N. D. Bertyaeva and V. B. Pen’kov, “Solution of mixed problems of elasticity for an anisotropic half-plane and interfaced half-planes,” Prikl. Mat. Mekh., 68, No. 1, 35–44 (2003).
Yu. A. Brychkov, “On the smoothness of solutions of linear partial differential equations in some of the variables,” Diff. Uravn., 10, No. 2, 281–289 (1974).
D. F. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).
A. F. Krivoi and M. V. Radiollo, “Singularities of the stress field near inclusions in a compound anisotropic plane,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 3, 84–92 (1984).
A. F. Krivoi, “Arbitrarily oriented defects in a compound anisotropic plane,” Visn. Odes. Derzh. Univ., Fiz.-Mat. Nauky, 6, No. 3, 108–115 (2001).
O. F. Kryvyi and K. M. Arkhipenko, “A crack that reaches the interface between two dissimilar anisotropic half-planes,” Mat. Metody Fiz.-Mekh. Polya, 48, No. 3, 110–116 (2005).
A. F. Krivoi, “Fundamental solution for a four-component anisotropic plane,” Visn. Odes. Derzh. Univ., Fiz.-Mat. Nauky, 8, No. 2, 140–149 (2003).
S. G. Lekhnitskii, Anisotropic Elasticity Theory [in Russian], Nauka, Moscow (1977).
V. V. Loboda and A. E. Sheveleva, “Determining prefracture zones at a crack tip between two elastic orthotropic bodies,” Int. Appl. Mech., 39, No. 5, 566–572 (2003).
S. A. Nazarov, “Crack at the interface between anisotropic bodies. Singularities of elastic fields and failure criteria for contacting crack faces,” Prikl. Mat. Mekh., 69, No. 3, 520–532 (2005).
G. Ya. Popov, Concentration of Elastic Stresses near Punches, Notches, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).
K. F. Chernykh, An Introduction to Anisotropic Elasticity [in Russian], Nauka, Moscow (1988).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 1. Problem formulation and basic relations,” Int. Appl. Mech., 38, No. 4, 423–431 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 2. Exact solution. The case of unequal roots,” Int. Appl. Mech., 38, No. 5, 548–555 (2002).
K. P. Herrmann and V. V. Loboda, “On interface crack models with contact zones situated in an anisotropic biomaterial,” Arch. Appl. Mech., 69, 317–335 (1999).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 36–45, June 2008.
Rights and permissions
About this article
Cite this article
Krivoi, A.F., Popov, G.Y. Features of the stress field near tunnel inclusions in an inhomogeneous anisotropic space. Int Appl Mech 44, 626–634 (2008). https://doi.org/10.1007/s10778-008-0084-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-008-0084-4