Exact and complete fundamental solutions for penny-shaped crack in an infinite transversely isotropic thermoporoelastic medium: mode I problem
![]() ![]() |
LI, Xiang-Yu
(School of Mechanics and Engineering, Southwest Jiaotong University)
Wu, J. (Laboratoire d'Etudes Aerodynamiques, Universite de Poitiers) Chen, W.Q. (Department of Engineering Mechanics, Zhejiang University) Wang, Hui-Ying (E.N.S.M.A., University of Poitiers) Zhou, Z.Q. (Department of Mechanical and Aerospace Engineering, University of Miami) |
1 | Abousleiman, Y. and Ekbote, S. (2000), "Porothermoelasticity in transversely isotropic porous materials", IUTAM Symposium on Theoretical and Numerical Method in Continuum Mechanics of Porous Materials, 145-152. |
2 | Abousleiman, Y., Cheng, A.H.D., Cui, L., Detournay, E. and Roegiers, J.C. (1996), "Mandel's problem revisited", Geotechnique, 46, 187-195. DOI ScienceOn |
3 | Adelaide, F.F., Bui, H.D. and Ehrlacher, A. (2003), "Hydrostatic interaction of a wetting fluid and a circular crack in an elastic material", Mech. Mater., 35, 581-586. DOI ScienceOn |
4 | Atkinson, C. and Craster, R.V. (1991), "Plane strain fracture in poroelastic media", Proc. Roy. Soc. London. A434, 605-633. |
5 | Biot, M.A. (1941), "General solutions of three-dimensional consolidation", J. Appl. Phys., 12, 155-164. DOI |
6 | Biot, M.A. (1955), "Theory of elasticity and consolidation for a porous anisotropic solid", J. Appl. Phys., 26, 182-185. DOI |
7 | Boone, T.J. and Detournay, E. (1990), "Response of a vertical hydraulic fracture intersecting a poroelastic formation bounded by a semi-infinite impermeable elastic layer", Int. J. Rock. Mech. Min. Sci. Geomech. Abstr., 27, 189-197. DOI ScienceOn |
8 | Chen, J. (1994a), "Time domain fundamental solution to Biot's complete equations of poroelasticity: Part I twodimensional solution", Int. J. Solids Struct., 31, 1447-1490. DOI ScienceOn |
9 | Chen, J. (1994b), "Time domain fundamental solution to Biot's complete equations of poroelasticity: Part II three-dimensional solution", Int. J. Solids Struct., 3, 169-202. |
10 | Chen, W.Q. and Ding, H.J. (2004), "Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey", J. Zhejiang Univ. SCI., 5(9), 1009-1021. DOI ScienceOn |
11 | Chen, W.Q., Ding, H.J. and Ling, D.S. (2004), "Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution", Int. J. Solids Struct., 41, 69-83. DOI ScienceOn |
12 | Cheng, A.H.D. and Detournay, E. (1988), "A direct boundary element for plane strain poroelasticity", Int. J. Numer. Anal. Meth. Geomech., 12, 551-572. DOI ScienceOn |
13 | Cheng, A.H.D. and Liggett, J.A. (1984a), "Boundary integral equation method for linear porous-elasticity with applications to soil consolidation", Int. J. Numer. Meth. Eng., 20, 255-278. DOI ScienceOn |
14 | Cheng, A.H.D. and Liggett, J.A. (1984b), "Boundary integral equation method for linear porous-elasticity with applications to fracture propagation", Int. J. Numer. Meth. Eng., 20, 279-296. DOI ScienceOn |
15 | Fabrikant, V.I. (1989), "Applications of potential theory in mechanics: A selection of new results", Kluwer Academic Publishers, The Netherlands. |
16 | Cleary, M.P. (1977), "Fundamental solutions for a fluid-saturated porous solid", Int. J. Solids Struct., 13, 785-806. DOI ScienceOn |
17 | Coussy, O. (1995), Poromechanics, John Wiley & Sons, Ltd. |
18 | Ding, H.J., Chen, W.Q. and Zhang, L.C. (2006), Elasticity of Transversely Isotropic Materials, Springer, Dordrecht. |
19 | Gatmiri, B. and Jabbari, E. (2005a), "Time-domain Green's functions for unsaturated soils. Part I: Twodimensional solution", Int. J. Solids Struct., 42, 5971-5990. DOI ScienceOn |
20 | Gatmiri, B. and Jabbari, E. (2005b), "Time-domain Green's functions for unsaturated soils. Part II: Threedimensional solution", Int. J. Solids Struct., 42, 5991-6002. DOI ScienceOn |
21 | Gatmiri, B. and Nguyen, K.V. (2005), "Time 2D fundamental solution for saturated porous media with incompressible fluid", Commun. Numer. Meth. Eng., 21(3), 119-132. |
22 | Gibson, R.E. (1967), "Some results concerning displacements and stresses in a non-homogeneous elastic halfspace", Geotechnique, 17, 58-67. DOI |
23 | Gibson, R.E. and McNamee, J. (1963), "A three-dimensional problem of consolidation of a semi-infinite clay stratum", Quart. J. Mech. Appl. Math., 16, 115-127. DOI |
24 | Gordeyev, Y.N. (1995), "A hydraulic fracture in a transversely isotropic poroelastic medium", J. Appl. Math. Mech., 59, 645-656. DOI ScienceOn |
25 | Gradsbteyn, I.S. and Ryzbik, L.M. (2004), Table of Integrals, Series, and Products, 6th edition, Elsevier, Pte. Ltd., Singapore. |
26 | Kanj, M. and Abousleiman, Y. (2005), "Porothermoelastic analyses of anisotropic hollow cylinders with applications", Int. J. Numer. Anal. Meth. Geomech., 29, 103-126. DOI ScienceOn |
27 | Norris, A.N. (1985), "Radiation from a point source and scattering theory in a fluid-saturated porous solid", J. Acoustic. Soc. Am., 77, 2012-2023. DOI |
28 | Li, X.Y., Chen, W.Q. and Wang, H.Y. (2010), "General steady state solutions for transversely isotropic thermoporoelastic media in three dimensions and its application", Eur. J. Mech. A/Solids, 29, 317-326. DOI ScienceOn |
29 | Liu, L. and Kardomateas, G.A. (2005), "Thermal stress intensity factors for a crack in an anisotropic half plane", Int. J. Solids Struct., 42, 5208-5223. DOI ScienceOn |
30 | Nowacki, W. (1966), "Green's functions for a thermoelastic medium (quasi-static problem)", Buletinul Institutului Politehnic din Iasi, Serie Noua12, 83-92. |
31 | Singh, B.M., Danyluk, H.T. and Selvachurai, A.P.S. (1987), "Thermal stresses in a transversely isotropic elastic solid weakened by an external circular crack", Int. J. Solids Struct., 23, 403-412. DOI ScienceOn |
![]() |