The earlier developed method of direct cutting-out is extended to the class of problems of elastic equilibrium of piecewise homogeneous bodies with internal and interface crack-like defects under antiplane deformation. This method is based on modeling of the initial problem for a body with thin inclusions (in particular, cracks) by a simpler problem of elastic equilibrium of piecewise homogeneous space with elevated number of thin defects, which, in fact, form new boundaries of the analyzed body. The reliability of the proposed approach is checked on examples of problems of longitudinal shear for a piecewise homogeneous wedge, a piecewise homogeneous half space, and a two-layer strip with interface crack subjected to the action of homogeneous loads and concentrated forces.
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References
V. V. Bozhydarnyk and H. T. Sulym, Elements of the Theory of Plasticity and Strength [in Ukrainian], Svit, Lviv (1999).
K. V. Vasil’ev and H. T. Sulym, “Application of the method of direct cutting-out to the solution of the problem of longitudinal shear of a wedge with thin heterogeneities of arbitrary orientation,” Mat. Metody Fiz.-Mekh. Polya, 53, No. 3, 117–126 (2010); English translation: J. Math. Sci., 180, No. 2, 122–134 (2012).
K. Vasil’ev, Ya. Pasternak, and H. Sulym, “Antiplane deformation of a square (in plan) body with thin internal inhomogeneity,” Visn. L’viv. Univ., Ser. Mekh.-Mat., Issue 73, 165–176 (2010).
K. Vasil’ev and H. Sulym, “Direct method of cutting-out in modeling the stress-strain state of isotropic layered media with thin inhomogeneities under the conditions of antiplane deformation,” Mashynoznavstvo, No. 11–12, 10–17 (2006).
K. Vasil’ev and H. Sulym, “Solution of integral equations of the problems for layered media with arbitrarily oriented strip inhomogeneities by the collocation method,” Visn. L’viv. Univ., Ser. Prykl. Mat. Inform., Issue 15, 157–169 (2009).
Ya. Pasternak, H. Sulym, and N. Oliyarnyk, “Boundary-element method in the problems of antiplane deformation of anisotropic bodies with thin inhomogeneities,” Visn. L’viv. Univ., Ser. Mekh.-Mat., Issue 76, 119-133 (2012).
H. T. Sulym, Foundations of the Mathematical Theory of Thermoelastic Equilibrium of Deformable Solids with Thin Inclusions [in Ukrainian], Doslid.-Vydavnych. Tsentr NTSh, Lviv (2007).
H. G. Beom and H. S. Jang, “Interfacial wedge cracks in dissimilar anisotropic materials under antiplane shear,” Int. J. Eng. Sci., 56, 49–62 (2012).
C.-H. Chen, C.-C. Ke, and C.-L. Wang, “Interface stress intensity factors for edge-cracked bonded semicircles and strips under outof-plane shear,” Int. J. Fract., 180, No. 1, 119–127 (2013).
F. Erdogan and G. D. Gupta, “Bonded wedges with an interface crack under anti-plane shear loading,” Int. J. Fract., 11, No. 4, 583–593 (1975).
X.-F. Li, “Closed-form solution for a mode-III interface crack between two bonded dissimilar elastic layers,” Int. J. Fract., 109, No. 2, 3–8 (2001).
L. P. Pook, “A finite element analysis of cracked square plates and bars under antiplane loading,” Fatigue Fract. Eng. Mater. Struct., 26, No. 6, 533–541 (2003).
A. R. Shahani, “Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials,” Arch. Appl. Mech., 75, No. 6, 405–411 (2006).
A. R. Shahani, “Some problems in the antiplane shear deformation of bimaterial wedges,” Int. J. Solids Struct., 42, No. 11-12, 3093–3113 (2005).
X. D. Wang and S. A. Meguid, “The interaction between an interfacial crack and a microcrack under antiplane loading,” Int. J. Fract., 76, No. 3, 263–278 (1996).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 59, No. 4, pp. 44–57, October–December, 2016.
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Vasil’ev, К.V., Sulym, H.T. Method of Direct Cutting-Out in the Problems of Piecewise Homogeneous Bodies with Interface Cracks Under Longitudinal Shear. J Math Sci 238, 46–62 (2019). https://doi.org/10.1007/s10958-019-04217-w
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DOI: https://doi.org/10.1007/s10958-019-04217-w