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Intensity of Dynamic Stresses of Longitudinal Shear in a Periodically Layered Composite with Penny-Shaped Cracks

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We consider the problem of harmonic torsional loading of an infinite elastic composite formed by alternating plane layers made of two different materials in the presence of a penny-shaped crack in one of the components of periodic structure. By using the integral representations for displacements and stresses in the frequency domain and satisfying the conditions of periodicity and perfect contact on the interfaces, we deduce a system of uncoupled boundary integral equations for the functions of tangential dynamic crack-opening displacement in a two-layered representative element of the composite. We perform the numerical analysis of the mode-III dynamic stress intensity factors in the vicinity of the analyzed crack depending on the wave number, the thicknesses of constituent layers, and the properties of their materials.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    V. Z. Stankevych & V. V. Mykhas’kiv

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  1. V. Z. Stankevych
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  2. V. V. Mykhas’kiv
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Correspondence to V. Z. Stankevych.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 3, pp. 46–54, July–September, 2020.

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Stankevych, V.Z., Mykhas’kiv, V.V. Intensity of Dynamic Stresses of Longitudinal Shear in a Periodically Layered Composite with Penny-Shaped Cracks. J Math Sci 273, 51–60 (2023). https://doi.org/10.1007/s10958-023-06483-1

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