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Fracture by Axial Compression of a Continuous Cylinder Weakened by a Cylindrical Crack near Its Surface

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Abstract

Based on a nonclassical criterial approach associated with the mechanism for local loss of stability in the neighborhood of a defect, a method is proposed for solving problems related to the fracture of a compressible elastic cylinder with a cylindrical crack near its surface for large subcritical deformations. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a uniform system of linear algebraic equations in the contraction parameter.

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REFERENCES

  1. A. N. Guz', Mechanics of Brittle Fracture of Materials with Initial Stresses [in Russian], Kiev (1983).

  2. A. N. Guz', Elements of the Three-Dimensional Theory of Stability of Deformed Bodies [in Russian], Kiev (1986).

  3. A. N. Guz', V. M. Nazarenko, and Yu. I. Khoma, “Fracture of an infinite incompressible hyperelastic material during compression along a cylindrical crack, ” Prikl. Mekh., 32, No. 5, 3–10 (1996).

    Google Scholar 

  4. Yu. I. Khoma, “Method for studying fracture of bodies with a cylindrical cavity and a coaxial cylindrical crack of finite length under axial compression, ” Teor. Prikl. Mekh., No. 30, 76–84 (1999).

  5. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, NBS, Washington, DC (1979).

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  6. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], 4th ed., Moscow (1963).

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Authors and Affiliations

  1. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    Yu. I. Khoma

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  1. Yu. I. Khoma
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Khoma, Y.I. Fracture by Axial Compression of a Continuous Cylinder Weakened by a Cylindrical Crack near Its Surface. Journal of Mathematical Sciences 103, 314–319 (2001). https://doi.org/10.1023/A:1011301926127

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  • DOI: https://doi.org/10.1023/A:1011301926127

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