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[1] Xiaoping, L. & Wei-Liang, W., A new subregion boundary element technique based on the domain decomposition method. Engineering Analysis with Boundary Elements, 29, pp. 944–952, 2005. [Crossref]
[2] Gao, X-W., Guo, L. & Zhang, C., Three-step multi-domain BEM solver for nonho-mogeneous material problems. Engineering Analysis with Boundary Elements, 31, pp. 965–973, 2007. [Crossref]
[3] Ribeiro, D.B. & Paiva, J.B., An alternative multi-region BEM technique for three-dimensional elastic problems. Engineering Analysis with Boundary Elements, 33, pp. 499–507, 2009. [Crossref]
[4] Ramšak, M. & Škerget, L., 3D multidomain BEM for solving the Laplace equation. Engineering Analysis with Boundary Elements, 31, pp. 528–538, 2007. [Crossref]
[5] Ramšak, M. & Škerget, L., 3D multidomain BEM for a poisson equation. Engineering Analysis with Boundary Elements, 33, pp. 689–694, 2009. [Crossref]
[6] Gao, X-W. & Wang, J., Interface integral BEM for solving multi-medium heat conduc-tion problems. Engineering Analysis with Boundary Elements, 33, pp. 539–546, 2009. [Crossref]
[7] Ramšak, M. & Škerget, L., A multidomain boundary element method for two equation tur-bulence models. Engineering Analysis with Boundary Elements, 29, pp. 1086–1103, 2005. [Crossref]
[8] Davi, G. & Milazzo, A., Multidomain boundary integral equation for piezoelec-tric materials fracture mechanics. International Journal of Solids and Structures, 38, pp. 7065–7078, 2001. [Crossref]
[9] Galvis, A.F. & Sollero, P., Boundary element analysis of crack problems in polycrystal-line materials. Procedia Materials Science, 3, pp. 1928–1933, 2014. [Crossref]
[10] Phan, A.-V. & Mukherjee, S., The multi-domain boundary contour method for interface and dissimilar material problems. Engineering Analysis with Boundary Elements, 33, pp. 668–677, 2009. [Crossref]
[11] Zhao, Y.F., Zhao, M.H. & Pan, E., Displacement discontinuity analysis of a nonlinear interfacial crack in three-dimensional transversely isotropic magneto-electro-elastic bi-materials. Engineering Analysis with Boundary Elements, 61, pp. 254–264, 2015. [Crossref]
[12] Lei, J., Garcia-Sanchez, F., Wünsche, M., Zhang, C., Wang, Y.-S. & Saez, A., Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM. Engineering Analysis with Boundary Elements, 76, pp. 1996–2010, 2009. [Crossref]
[13] Lei, J., Garcia-Sanchez, F. & Zhang, C., Determination of dynamic intensity factors and time-domain BEM for interfacial cracks in anisotropic piezoelectric materials. Interna-tional Journal of Solids and Structures, 50, pp. 1482–1493, 2013. [Crossref]
[14] Yang, B., Pan, E. & Tewary, V.K., Three-dimensional Green’s functions of steady-state motion in anisotropic half-spaces and bimaterials. Engineering Analysis with Boundary Elements, 28, pp. 1069–1082, 2004. [Crossref]
[15] Kassir, M.K. & Sih, G.C., Three Dimensional Crack Problems, Noordhoff: Leyden, 1975.
[16] Pavlou, D.G., Boundary-integral equation analysis of twisted internally cracked axi-symmetric biomaterial elastic solids. Computational Mechanics, 29, pp. 254–264, 2002. [17] Pavlou, D.G., Green’s functions for the biomaterial elastic solid containing interface crack. Engineering Analysis with Boundary Elements, 26, pp. 845–853, 2002. http://dx.doi.org/10.1016/S0955-7997(02)00052-8 [Crossref]
[17] Pavlou, D.G., Green’s functions for the biomaterial elastic solid containing interface crack. Engineering Analysis with Boundary Elements, 26, pp. 845–853, 2002. [Crossref]
[18] Mavrothanasis, F.I. & Pavlou, D.G., Mode-I stress intensity factor derivation by a suitable Green’s function. Engineering Analysis with Boundary Elements, 31, pp. 184–190, 2007. [Crossref]
[19] Mavrothanasis, F.I. & Pavlou, D.G., Green’s function for KI determination of axisym-metric elastic solids containing external circular crack. Engineering Fracture Mechan-ics, 75, pp. 1891–1905, 2008. [Crossref]
[20] Kermanidis, T., A numerical solution for axially symmetric elasticity problems. Inter-national Journal of Solids and Structures, 11, pp. 493–500, 1975. [Crossref]
[21] Bakr, A.A. & Fenner, R.T., Use of the Hankel transform in boundary integral methods for axisymmetric problems. International Journal of Numerical Methods in Engineer-ing, 19, pp. 1765–1769, 1983. [Crossref]
[22] Gradshteyn, I.S. & Ryzhik, I.M., Table of Integrals, Series, and Products, Academic Press: New York, 2000.
[23] Hasegawa, H., Green’s functions for axisymmetric surface force problems of an elastic half-space and their application. Theoretical and Applied Mechanics, 32, pp. 291–300, 1984.
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Open Access
Research article

Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources

d.g. pavlou
Department of Mechanical and Structural Engineering and Materials Science, University of Stavanger, Norway
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 215-230
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

A review of Green’s functions for dissimilar or homogeneous elastic space containing penny-shaped or annular interfacial cracks under singular ring-shaped loading sources is presented. The solutions are based on fictitious singular loading sources and superposition of the fundamental solutions of the following two problems: (a) Dissimilar elastic solid without crack under singular source, and (b) Dis-similar elastic solid containing crack under surface tractions. The above Green’s functions have the following advantages: (i) No multi-region BE modeling for the dissimilar material is necessary, and (ii) No discretization of the crack surface is necessary. Numerical examples are presented and discussed.

Keywords: Axisymmetric loading, Crack, Dissimilar material, Green’s functions

1. Introduction

2. Loading Sources

3. A Review of Green’s Functions

4. Numerical Results

5. Conclusions

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Xiaoping, L. & Wei-Liang, W., A new subregion boundary element technique based on the domain decomposition method. Engineering Analysis with Boundary Elements, 29, pp. 944–952, 2005. [Crossref]
[2] Gao, X-W., Guo, L. & Zhang, C., Three-step multi-domain BEM solver for nonho-mogeneous material problems. Engineering Analysis with Boundary Elements, 31, pp. 965–973, 2007. [Crossref]
[3] Ribeiro, D.B. & Paiva, J.B., An alternative multi-region BEM technique for three-dimensional elastic problems. Engineering Analysis with Boundary Elements, 33, pp. 499–507, 2009. [Crossref]
[4] Ramšak, M. & Škerget, L., 3D multidomain BEM for solving the Laplace equation. Engineering Analysis with Boundary Elements, 31, pp. 528–538, 2007. [Crossref]
[5] Ramšak, M. & Škerget, L., 3D multidomain BEM for a poisson equation. Engineering Analysis with Boundary Elements, 33, pp. 689–694, 2009. [Crossref]
[6] Gao, X-W. & Wang, J., Interface integral BEM for solving multi-medium heat conduc-tion problems. Engineering Analysis with Boundary Elements, 33, pp. 539–546, 2009. [Crossref]
[7] Ramšak, M. & Škerget, L., A multidomain boundary element method for two equation tur-bulence models. Engineering Analysis with Boundary Elements, 29, pp. 1086–1103, 2005. [Crossref]
[8] Davi, G. & Milazzo, A., Multidomain boundary integral equation for piezoelec-tric materials fracture mechanics. International Journal of Solids and Structures, 38, pp. 7065–7078, 2001. [Crossref]
[9] Galvis, A.F. & Sollero, P., Boundary element analysis of crack problems in polycrystal-line materials. Procedia Materials Science, 3, pp. 1928–1933, 2014. [Crossref]
[10] Phan, A.-V. & Mukherjee, S., The multi-domain boundary contour method for interface and dissimilar material problems. Engineering Analysis with Boundary Elements, 33, pp. 668–677, 2009. [Crossref]
[11] Zhao, Y.F., Zhao, M.H. & Pan, E., Displacement discontinuity analysis of a nonlinear interfacial crack in three-dimensional transversely isotropic magneto-electro-elastic bi-materials. Engineering Analysis with Boundary Elements, 61, pp. 254–264, 2015. [Crossref]
[12] Lei, J., Garcia-Sanchez, F., Wünsche, M., Zhang, C., Wang, Y.-S. & Saez, A., Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM. Engineering Analysis with Boundary Elements, 76, pp. 1996–2010, 2009. [Crossref]
[13] Lei, J., Garcia-Sanchez, F. & Zhang, C., Determination of dynamic intensity factors and time-domain BEM for interfacial cracks in anisotropic piezoelectric materials. Interna-tional Journal of Solids and Structures, 50, pp. 1482–1493, 2013. [Crossref]
[14] Yang, B., Pan, E. & Tewary, V.K., Three-dimensional Green’s functions of steady-state motion in anisotropic half-spaces and bimaterials. Engineering Analysis with Boundary Elements, 28, pp. 1069–1082, 2004. [Crossref]
[15] Kassir, M.K. & Sih, G.C., Three Dimensional Crack Problems, Noordhoff: Leyden, 1975.
[16] Pavlou, D.G., Boundary-integral equation analysis of twisted internally cracked axi-symmetric biomaterial elastic solids. Computational Mechanics, 29, pp. 254–264, 2002. [17] Pavlou, D.G., Green’s functions for the biomaterial elastic solid containing interface crack. Engineering Analysis with Boundary Elements, 26, pp. 845–853, 2002. http://dx.doi.org/10.1016/S0955-7997(02)00052-8 [Crossref]
[17] Pavlou, D.G., Green’s functions for the biomaterial elastic solid containing interface crack. Engineering Analysis with Boundary Elements, 26, pp. 845–853, 2002. [Crossref]
[18] Mavrothanasis, F.I. & Pavlou, D.G., Mode-I stress intensity factor derivation by a suitable Green’s function. Engineering Analysis with Boundary Elements, 31, pp. 184–190, 2007. [Crossref]
[19] Mavrothanasis, F.I. & Pavlou, D.G., Green’s function for KI determination of axisym-metric elastic solids containing external circular crack. Engineering Fracture Mechan-ics, 75, pp. 1891–1905, 2008. [Crossref]
[20] Kermanidis, T., A numerical solution for axially symmetric elasticity problems. Inter-national Journal of Solids and Structures, 11, pp. 493–500, 1975. [Crossref]
[21] Bakr, A.A. & Fenner, R.T., Use of the Hankel transform in boundary integral methods for axisymmetric problems. International Journal of Numerical Methods in Engineer-ing, 19, pp. 1765–1769, 1983. [Crossref]
[22] Gradshteyn, I.S. & Ryzhik, I.M., Table of Integrals, Series, and Products, Academic Press: New York, 2000.
[23] Hasegawa, H., Green’s functions for axisymmetric surface force problems of an elastic half-space and their application. Theoretical and Applied Mechanics, 32, pp. 291–300, 1984.
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Pavlou, D. (2017). Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources. Int. J. Comput. Methods Exp. Meas., 5(3), 215-230. https://doi.org/10.2495/CMEM-V5-N3-215-230
D. Pavlou, "Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 215-230, 2017. https://doi.org/10.2495/CMEM-V5-N3-215-230
@research-article{Pavlou2017Green’sFF,
title={Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources},
author={D.G. Pavlou},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={215-230},
doi={https://doi.org/10.2495/CMEM-V5-N3-215-230}
}
D.G. Pavlou, et al. "Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources." International Journal of Computational Methods and Experimental Measurements, v 5, pp 215-230. doi: https://doi.org/10.2495/CMEM-V5-N3-215-230
D.G. Pavlou. "Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 215-230. doi: https://doi.org/10.2495/CMEM-V5-N3-215-230
PAVLOU DG. Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, under Axisymmetric Singular Loading Sources[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 215-230. https://doi.org/10.2495/CMEM-V5-N3-215-230