Abstract
The present work deals with the application of spring boundary conditions in order to describe elastic wave propagation in composites with damaged interfaces. Dynamic behaviour of the damaged zone is described by means of a distribution of micro-cracks and introduction of spring boundary conditions, where stresses are proportional to the jump in displacement along the damaged interface and the proportionality factor is the distributed spring stiffness. The stiffness in the spring boundary conditions is determined from the equivalence of the transmission coefficients for these two models. As a result, the normal and tangential components of the spring stiffness tensor depend on the concentration of the defects , their typical size and elastic properties of the contacting materials. The three-dimensional problem with elastic wave scattering by a random or periodic distribution of rectangular microcracks is considered, the latter with a boundary integral equation method. The transmission through the damaged interface with random and periodic distribution of rectangular cracks is compared with a good correspondence giving confidence that the models are appropriate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
I. Solodov, J. Bai, G. Busse, J. Appl. Phys. 113, 223512 (2013)
D.A. Sotiropoulos, J.D. Achenbach, J. Nondestr. Eval. 7, 123 (1988)
M. Kachanov, Adv. Appl. Mech. 30, 259 (1994)
J.-M. Baik, R.B. Thompson, J. Nondestr. Eval. 4, 177 (1984)
S. Gopalakrishnan, A. Chakraborty, D.R. Mahapatra, Spectral Finite Element Method: Wave Propagation, Diagnostics and Control in Anisotropic and Inhomogeneous Structures (Springer-Verlag London Limited, 2008), 449pp
Y.V. Glushkov, N.V. Glushkova, A.V. Yekhlakov, J. Appl. Math. Mech. 66(1), 141 (2002)
A. Boström, G.R. Wickham, J. Nondestr. Eval. 10, 139 (1991)
M.V. Golub, A. Boström, Wave Motion 48(2), 105 (2011)
E. Glushkov, N. Glushkova, J. Comput. Acoust. 9, 889 (2001)
M.V. Golub, O.V. Doroshenko, A. Boström, Int. J. Solids Struct. 81, 141 (2016)
V. Mykhas’kiv, I. Zhbadynskyi, C. Zhang, J. Math. Sci. 203, 114 (2014)
M.Y. Remizov, M.A. Sumbatyan, Math. Mech. Solids 22, 1 (2017)
M.V. Golub, O.V. Doroshenko, Math. Mech. Solids, December (2017)
E. Glushkov, J. Appl. Math. Mech. 47, 70 (1983)
V. Babich, A. Kiselev, Elastic Waves. A High-Frequency Theory (BHV-Petersburg, 1981) (in Russian)
Y. Ishii, S. Biwa, J. Acoust. Soc. Am. 141, 1099 (2017)
Acknowledgements
The work is supported by the Russian Science Foundation (Project 17-11-01191), which is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Golub, M.V., Boström, A.E., Doroshenko, O.V. (2018). Modelling of Elastic Wave Propagation Through Damaged Interface via Effective Spring Boundary Conditions. In: Parinov, I., Chang, SH., Gupta, V. (eds) Advanced Materials . PHENMA 2017. Springer Proceedings in Physics, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-319-78919-4_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-78919-4_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78918-7
Online ISBN: 978-3-319-78919-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)