Abstract
Dynamics response of an elliptical cavity and a crack (on different sides) near bimaterials interface under incident out-plane waves is studied by applying the methods of complex variables and Green’s function. Firstly, based on “conjunction,” the analytical model is divided along the horizontal interface into an elastic half-plane possessing an elliptical cavity and a full elastic half-plane containing a crack. Using complex variables, the scattering displacement field of the half-plane containing an elliptical cavity under incident out-plane waves is then derived. According to the method of Green’s function, the corresponding Green’s functions of two half-planes impacted by an out-plane source load are further deduced. Combined with “crack division,” a crack at the full elastic the half-plane is created, and thus, expressions of displacement and stress are derived while the cavity coexists with the crack. Undetermined antiplane forces are loaded on the horizontal surfaces for conjunction of two sections and then solved by a series of Fredholm integral equations on account of continuity conditions of the interface. Finally, this paper focuses on the discussion of the influence law of different parameters on the dynamics response of complex defects near bimaterials interface by comprehensive numerical results.
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Pao Y.H., Mow C.C.: Diffraction of elastic waves and dynamic stress concentrations, pp. 114–304. Crane and Russak, New York (1973)
Liu D.K., Gai B.Z., Tao G.Y.: Applications of the method of complex variables to dynamic stress concentrations. Wave Motion 4, 293–304 (1982)
Chen T.Y., Wang H.: Dynamic analysis of upright incident of SH-waves at semi-cylindrical interface with a circular lining structure. J. Tianjin Univ. 39, 1305–1309 (2006)
Wang G.Q., Liu D.K.: Scattering of SH-wave by multiple circular cavities in half space. Earthq. Eng. Eng. Vib. 1, 36–44 (2002)
Xu P., Tie Y., Xia T.D.: Scattering of plane SH Waves by two separated circular tunnel linings. Northwest. Seismol. J. 30, 145–149 (2008)
Liu D.K., Lin H.: Scattering of SH-waves by circular cavities near biomaterial interface. Acta Mech. Solida Sin. 24, 197–204 (2003)
Liu D.K., Lin H.: Scattering of SH-waves by an interface linear crack and a circular cavity near bimaterial interface. Acta Mech. Sin. 20, 317–326 (2004)
Yang, Z.L., Chen, Z.G., Liu, D.K.: Scattering of SH-wave by an interacting mode III crack and a circular cavity in half space. Key Eng. Mater. 348–349, 861–864 (2007) (2007)
Yang Z.L., Yan P.L., Liu D.K.: Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space. Chin J. Theor. Appl. Mech. 41, 229–235 (2009)
Lu J.F., Wang Y.S., Cai L.: Scattering of SH wave by a crack terminating at the interface of bi-material. Chin J. Theor. Appl. Mech. 35, 432–436 (2003)
Rodriguez-Castellanos A., Luzon F., Sanchez-Sesma F.J.: Diffraction of seismic waves in an elastic cracked half plane using boundary integral formulation. Soil Dyn. Earthq. Eng. 25, 827–837 (2005)
Tsaur D.H., Chang K.H.: Multiple scattering of SH waves by an embedded truncated circular cavity. J. Mar. Sci. Technol. 20, 73–81 (2012)
Wang Y.S., Qiu Z.Y., Yu G.L.: Scattering of SH waves from a partially debonded rigid elliptic cylinder. Soil. Dyn. Earthq. Eng. 21, 139–149 (2001)
Coussy O.: Scattering of elastic waves by an inclusion with an interface crack. Wave Motion 6, 223–236 (1984)
Bair V.B., David B.B.: Wave scattering by surface-breaking cracks and cavities. Wave Motion 40, 163–172 (2004)
Tanimura S.: Stress wave propagation in elastic/viscoplastic cylindrical bodies containing a spherical cavity. Acta Mech. 51, 1–13 (1984)
Yu C.W., Dravinski M.: Scattering of plane harmonic P, SV and Rayleigh waves by a completely embedded corrugated elastic inclusion. Wave Motion 47, 156–167 (2010)
Dravinski M., Sheikhhassani R.: Scattering of a plane harmonic SH wave by a rough multilayered inclusion of arbitrary shape. Wave Motion 50, 836–851 (2013)
Parvanova S., Dineva P., Manolis G.D.: Elastic wave fields in a half-plane with free-surface relief, tunnels and multiple buried inclusions. Acta Mech. 225, 1843–1865 (2014)
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Xu, Hn., Yang, Zl. & Wang, Ss. Dynamics response of complex defects near bimaterials interface by incident out-plane waves. Acta Mech 227, 1251–1264 (2016). https://doi.org/10.1007/s00707-015-1555-4
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DOI: https://doi.org/10.1007/s00707-015-1555-4