By solving boundary integral equations by the mapping method in combination with the step-by-step method of constructing time dependences, we have investigated the behavior of a compliant disk-shaped elliptic inclusion in a three-dimensional field of pulse elastic waves. In the case of a symmetric problem and nonstationary perturbation with the profile of the Heaviside function, we have established the influence of the eccentricity of the inclusion and the ratio of the elastic moduli of the matrix medium and inclusion on the dynamic stress intensity factor in the vicinity of the inclusion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Marukha, V. V. Panasyuk, and V. P. Sylovanyuk, Injection Technologies of Recovering the Workability of Damaged Durable Structures [in Ukrainian], Spolom, Lviv (2009).
V. V. Mykhas’kiv, Ya. I. Kunets’, and V. O. Mishchenko, “Stresses in a three-dimensional body with thin compliant inclusion behind the front of pulsed waves,” Fiz.-Khim. Mekh. Mater., 39, No. 3, 63–68 (2003); English translation: Mater. Sci., 39, No. 3, 377–384 (2003).
A. P. Moiseenok and V. G. Popov, “Interaction of plane nonstationary waves with a thin elastic inclusion under smooth contact conditions,” Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 152–164 (2009); English translations: Mech. Solids, 44, No. 4, 621–631 (2009).
M. P. Savruk, “New method for the solution of dynamic problems of the theory of elasticity and fracture mechanics,” Fiz.-Khim. Mekh. Mater., 39, No. 4, 7–11 (2003); English translation: Mater. Sci., 39, No. 4, 465–471 (2003).
V. P. Sylovanyuk and O. V. Halazyuk, “Numerical model of a body containing a crack “healed” by injection,” Fiz.-Khim. Mekh. Mater., 47, No. 2, 88–92 (2011); English translation: Mater. Sci., 47, No. 2, 211–216 (2011).
M. V. Khai, Two-Dimensional Integral Equations of Newton Potential Type and Their Applications [in Russian], Naukova Dumka, Kiev (1993).
A. Boström, P. Bövik, and P. Olsson, “A comparison of exact first order and spring boundary conditions for scattering by thin layers,” J. Nondestruct. Eval., 11, No. 3–4, 175–184 (1992).
V. V. Mykhas’kiv, “Transient response of a plane rigid inclusion to an incident wave in an elastic solid,” Wave Motion, 41, No. 2, 133–144 (2005).
J. Sladek, V. Sladek, V. V. Mykhas’kiv, and V. Z. Stankevych, “Application of mapping theory to boundary integral formulation of 3D dynamic crack problems,” Eng. Anal. Bound. Elem., 27, No. 3, 203–213 (2003).
M. Wünsche, C. Zhang., F. Garsía-Sánchez, A. Sáez, V. Sladek, and J. Sladek. “On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids,” Comput. Methods Appl. Mech. Eng., 198, No. 33–36, 2812–2824 (2009).
Z. M. Xiao and J. Luo, “Three-dimensional dynamic stress analysis on a penny-shaped crack interacting with a suddenly transformed spherical inclusion,” Int. J. Fract., 123, No. 1, 29–47 (2003).
H. Yoshikawa and M. Nishimura, “An improved implementation of time domain elastodynamic BIEM in 3D for large scale problems and its application to ultrasonic NDE,” Electr. J. Bound. Elem., 1, No. 2, 201–217 (2003).
C. Zhang and A. Savaidis, “3-D transient dynamic crack analysis by a novel time-domain BEM,” Comput. Model. Eng. Sci., 4, No. 5, 603–618 (2003).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 1, pp. 113–121, January–March, 2012.
Rights and permissions
About this article
Cite this article
Mykhas’kiv, V.V., Kalynyak, O.І. & Hrylytskyi, M.D. Nonstationary problem of incidence of an elastic wave on a compliant inclusion in the form of an elliptic disk. J Math Sci 190, 764–774 (2013). https://doi.org/10.1007/s10958-013-1286-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-013-1286-9