Bases of singular solutions in problems of mechanics of cracks
Tóm tắt
The mechanics of cracks serves as a remarkable example of a consistent application of the general results of the theory of elliptic boundary value problems to domains with piecewise smooth boundaries (see key papers [1–3] and also monographs [4, 5]). In the first place, this applies to the analysis of the behavior of stress-strain state in the vicinity of the crack tip and to operations involving the most important characteristics of this state, because explicit formulas that enable a reasonable prediction of the fracture process are available only for isotropic elastic materials. Meanwhile, the modern engineering practice involves the study of damages in anisotropic and composite bodies.
Tài liệu tham khảo
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V. G. Maz’ya and B. A. Plamenevskii, Estimates in L p and in Hölder Classes, and the Miranda-Agmon Maximum Principle for the Solutions of Elliptic Boundary Value Problems in Domains with Singular Points on the Boundary,” Math. Nachr. 81, 25–82 (1978).
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I. I. Argatov and S. A. Nazarov, “Energy Release Caused by the Kinking of a Crack in a Plane Anisotropic Solid Body,” Prikl. Mat. Mekh. 66(3), 502–514 (2002).
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V. G. Maz’ya, S. A. Nazarov, and B. A. Plamenevskii, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, Vol. 1 (Akademie, Berlin, 1991; Birkhäuse, Basel, 2000).
S. A. Nazarov, “An Asymptotic Model of the Griffith Criterion under Small Kinking and Curving of a Crack.” Doklady Mathematics 408(4), 476–480 (2006).
S. A. Nazarov, “Scenarios for the Quasistatic Growth of a Slightly Curved and Kinked Crack,” Prikl. Mat. Mekh. 72(3), 347–359 (2008).
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S. A. Nazarov, “A Quasistatic Model of the Evolution of an Interface Inside a Deformed Solid Body,” Prikl. Mat. Mekh. 70(3) 458–472 (2006).
S. A. Nazarov, “Thin Elastic Coatings and Surface Enthalpy,” Mechanics of Solids 42(5), 60–74 (2007).
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V. G. Maz’ya, S. A. Nazarov, and B. A. Plamenevskii, “On the Singularities of Solutions of the Dirichlet Problem in the Exterior of a Slender Cone,” Matem. Sbornik 122(4), 435–456 (1983).