Full Text:   <1681>

CLC number: O343.2; O343.8; TB39

On-line Access: 

Received: 2004-06-22

Revision Accepted: 2004-06-28

Crosschecked: 0000-00-00

Cited: 22

Clicked: 4026

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Bio-Design and Manufacturing  2022 Vol.5 No.9 P.1009~1021

10.1631/jzus.2004.1009


Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey


Author(s):  CHEN Wei-qiu, DING Hao-jiang

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   chenwq@ccea.zju.edu.cn

Key Words:  Potential theory method, Mixed boundary value problem, Multi-field coupled media


Share this article to: More

CHEN Wei-qiu, DING Hao-jiang. Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey[J]. Journal of Zhejiang University Science D, 2022, 5(9): 1009~1021.

@article{title="Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey",
author="CHEN Wei-qiu, DING Hao-jiang",
journal="Journal of Zhejiang University Science D",
volume="5",
number="9",
pages="1009~1021",
year="2022",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.1009"
}

%0 Journal Article
%T Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey
%A CHEN Wei-qiu
%A DING Hao-jiang
%J Journal of Zhejiang University SCIENCE D
%V 5
%N 9
%P 1009~1021
%@ 1869-1951
%D 2022
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.1009

TY - JOUR
T1 - Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey
A1 - CHEN Wei-qiu
A1 - DING Hao-jiang
J0 - Journal of Zhejiang University Science D
VL - 5
IS - 9
SP - 1009
EP - 1021
%@ 1869-1951
Y1 - 2022
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.1009


Abstract: 
This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Ashida, F., Noda, N., Okumura, I., 1993. General solution technique for transient thermoelasticity of transversely isotropic solids in cylindrical coordinates. Acta Mech., 101:215-230.

[2] Chen, W.Q., 1999a. Exact solution of a semi-infinite crack in an infinite piezoelectric body. Arch. Appl. Mech., 69:309-316.

[3] Chen, W.Q., 1999b. Inclined circular flat punch on a transversely isotropic piezoelectric half-space. Arch. Appl. Mech., 69:455-464.

[4] Chen, W.Q., 1999c. On the application of potential theory in piezoelasticity. J. Appl. Mech., 66:808-810.

[5] Chen, W.Q., Ding, H.J., 1999a. A penny-shaped crack in a transversely isotropic piezoelectric solid: modes II and III problems. Acta Mech. Sin., 15:52-58.

[6] Chen, W.Q., Ding, H.J., 1999b. Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere. Acta Mech. Solida Sin., 12:114-120.

[7] Chen, W.Q., Shioya, T., 1999a. Fundamental solution for a penny-shaped crack in a piezoelectric medium. J. Mech. Phys. Solids, 47:1459-1475.

[8] Chen, W.Q., Shioya, T., 1999b. Green’s functions of an external circular crack in a transversely isotropic piezoelectric medium. JSME Int. J., A42:73-79.

[9] Chen, W.Q., Shioya, T., Ding, H.J., 1999a. Integral equations for mixed boundary value problem of a piezoelectric half-space and the applications. Mech. Res. Commun., 26:583-590.

[10] Chen, W.Q., Shioya, T., Ding, H.J., 1999b. The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space. J. Appl. Mech., 66:764-771.

[11] Chen, W.Q., 2000a. On piezoelastic contact problem for a smooth punch. Int. J. Solids Struct., 37:2331-2340.

[12] Chen, W.Q., 2000b. On the general solution for piezothermoelasticity for transverse isotropy with application. J. Appl. Mech., 67:705-711.

[13] Chen, W.Q., Shioya, T., 2000. Complete and exact solutions of a penny-shaped crack in a piezoelectric solid: antisymmetric shear loadings. Int. J. Solids Struct., 37:2603-2619.

[14] Chen, W.Q., Shioya, T., Ding, H.J., 2000. A penny-shaped crack in piezoelectrics: resolved. Int. J. Fracture, 105:49-56.

[15] Chen, W.Q., Ding, H.J., Hou, P.F., 2001a. Exact solution of an external circular crack in a piezoelectric solid subjected to shear loading. J. Zhejiang Univ. SCIENCE, 2:9-14.

[16] Chen, W.Q., Shioya, T., Ding, H.J., 2001b. An antisymmetric problem of a penny-shaped crack in a piezoelectric medium. Arch. Appl. Mech., 71:63-73.

[17] Chen, W.Q., Ding, H.J., 2003. Three-dimensional general solution of transversely isotropic thermoelasticity and the potential theory method. Acta Mech. Sin., 35:578-583 (in Chinese).

[18] Chen, W.Q., Ding, H.J., Ling, D.S., 2004a. Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution. Int. J. Solids Struct., 41:69-83.

[19] Chen, W.Q., Lee, K.Y., Ding, H.J., 2004b. General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. Int. J. Eng. Sci., 42:1361-1379.

[20] Courant, R., Hilbert, D., 1953. Methods of Mathematical Physics. Interscience, New York.

[21] Ding, H.J., Chen, W.Q., 2001. Three Dimensional Problems of Piezoelasticity. Nova Science Publishers, New York.

[22] Ding, H.J., Chen, B., Liang, J., 1996. General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct., 33:2283-2298.

[23] Ding, H.J., Chen, B., Liang, J., 1997a. On the Green’s functions for two-phase transversely isotropic piezoelectric media. Int. J. Solids Struct., 34:3041-3057.

[24] Ding, H.J., Zou, D.Q., Liang, J., Chen, W.Q., 1997b. Transversely Isotropic Elasticity. Zhejiang University Press, Hangzhou (in Chinese).

[25] Ding, H.J., Hou, P.F., Guo, F.L., 1999. Elastic and electric fields for elliptical contact for transversely isotropic piezoelectric bodies. J. Appl. Mech., 66:560-562.

[26] Ding, H.J., Hou, P.F., Guo, F.L., 2000. The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials. Int. J. Solids Struct., 37:3201-3229.

[27] Elliott, H.A., 1948. Three-dimensional stress distributions in aeolotropic hexagonal crystals. Proc. Camb. Phil. Soc., 44:522-533.

[28] Fabrikant, V.I., 1986. A new approach to some problems in potential theory. ZAMM, 66:363-368.

[29] Fabrikant, V.I., 1989. Applications of Potential Theory in Mechanics: A Selection of New Results. Kluwer Academic Publishers, Dordrecht.

[30] Fabrikant, V.I., 1991. Mixed Boundary Value Problem of Potential Theory and Their Applications in Engineering. Kluwer Academic Publishers, Dordrecht.

[31] Fabrikant, V.I., Rubin, B.S., Karapetian, E.N., 1993. Half-plane crack under normal load: Complete solution. J. Eng. Mech., 119:2238-2251.

[32] Fabrikant, V.I., 1997a. Computation of the resultant forces and moments in elastic contact problems. Int. J. Eng. Sci., 35:681-698.

[33] Fabrikant, V.I., 1997b. Generalized method of images in the crack analysis. Int. J. Eng. Sci., 35:1159-1184.

[34] Fabrikant, V.I., 1998a. Relationship between the solutions to normal and tangential crack problems. Q. J. Mech. Appl. Math., 51:329-337.

[35] Fabrikant, V.I., 1998b. Stress intensity factors and displacements in elastic contact and crack problems. J. Eng. Mech., 124:991-999.

[36] Fabrikant, V.I., 1999. Two arbitrarily located normal forces and a penny-shaped crack: A complete solution. Math. Meth. Appl. Sci., 22:1201-1220.

[37] Fabrikant, V.I., 2000. Two tangential forces and a penny-shaped crack: A complete solution. J. Eng. Mech., 126:102-111.

[38] Fabrikant, V.I., 2001. Exact solution of external tangential contact problem for a transversely isotropic elastic half-space. Arch. Appl. Mech., 71:371-388.

[39] Fabrikant, V.I., 2004. Application of the generalized images method to contact problems for a transversely isotropic elastic layer. J. Strain Anal., 39:55-70.

[40] Hanson, M.T., 1992a. Interaction between an infinitesimal glide dislocation loop coplanar with a penny-shaped crack. Int. J. Solids Struct., 29:2669-2686.

[41] Hanson, M.T., 1992b. The elastic field for conical indentation including sliding friction for transversely isotropy. J. Appl. Mech., 59:S123-S130.

[42] Hanson, M.T., 1992c. The elastic field for spherical Hertzian contact including sliding friction for transversely isotropy. J. Tribology, 114:606-611.

[43] Hanson, M.T., 1992d. The elastic potentials for coplanar interaction between an infinitesimal prismatic dislocation loop and a circular crack for transversely isotropy. J. Appl. Mech., 59:S72-S78.

[44] Hanson, M.T., 1993. The elastic field for a sliding conical punch on an isotropic half-space. J. Appl. Mech., 60:557-559.

[45] Hanson, M.T., Johnson, T., 1993. The elastic field for spherical Hertzian contact of isotropic bodies revisited: Some alternative expressions. J. Tribology, 115:327-332.

[46] Hanson, M.T., 1994. The elastic field for an upright or tilted sliding circular flat punch on a transversely isotropic half space. Int. J. Solids Struct., 31:567-586.

[47] Hanson, M.T., Puja, I.W., 1997a. The elastic field resulting from elliptical Hertzian contact of transversely isotropic bodies: Closed form solutions for normal and shear loading. J. Appl. Mech., 64:457-465.

[48] Hanson, M.T., Puja, I.W., 1997b. The Reissner-Sagoci problem for the transversely isotropic half-space. J. Appl. Mech., 64:692-694.

[49] Hanson, M.T., Puja, I.W., 1998a. Elastic subsurface stress analysis for circular foundations. I. J. Eng. Mech., 124:537-546.

[50] Hanson, M.T., Puja, I.W., 1998b. Elastic subsurface stress analysis for circular foundations. II. J. Eng. Mech., 124:547-555.

[51] Hou, P.F., 2000. Three-Dimensional Contact and Fracture of Piezoelectric Bodies. Ph.D. Dissertation, Zhejiang University (in Chinese).

[52] Hou, P.F., Ding, H.J., Guan, F.L., 2001a. A penny-shaped crack in an infinite piezoelectric body under antisymmetric point loads. J. Zhejiang Univ. SCIENCE, 2:146-151.

[53] Hou, P.F., Ding, H.J., Guan, F.L., 2001b. Exact solution to the problem of a half-plane crack in a transversely isotropic piezoelectric body subjected to antisymmetric tangential point forces. Acta Mech. Solida Sin., 14:176-182.

[54] Hou, P.F., Ding, H.J., Guan, F.L., 2001c. Point forces and point charge applied to a circular crack in a transversely isotropic piezoelectric space. Theor. Appl. Frac. Mech., 36:245-262.

[55] Hou, P.F., Ding, H.J., Guan, F.L., 2002. Circular crack in a transversely isotropic piezoelectric space under point forces and point charges. Acta Mech. Sin., 18:159-169.

[56] Hou, P.F., Andrew, Y.T.L., Ding, H.J., 2003. The elliptical Hertzian contact of transversely isotropic magnetoelectroelastic bodies. Int. J. Solids Struct., 40:2833-2850.

[57] Huang, J.H., 1997. A fracture criterion of a penny-shaped crack in transversely isotropic piezoelectric media. Int. J. Solids Struct., 34:2631-2644.

[58] Kachanov, M., Karapetian, E., 1997. Three-dimensional interactions of a half-plane crack with point forces, dipoles and moments. Int. J. Solids Struct., 34:4101-4125.

[59] Kaczyński, A., Matysiak, S.J., 2003. On the three-dimensional problem of an interface crack under uniform heat flow in a biomaterial periodically-layered space. Int. J. Fract., 123:127-138.

[60] Karapetian, E., Hanson, T., 1994. Crack opening displacements and stress intensity factors caused by a concentrated load outside a circular crack. Int. J. Solids Struct., 31:2035-2052.

[61] Karapetian, E., Kachanov, M., 1996. Three-dimensional interactions of a circular crack with dipoles, centers of dilatation and moments. Int. J. Solids Struct., 33:3951-3967.

[62] Karapetian, E., Kachanov, M., 1998. Green’s functions for the isotropic or transversely isotropic space containing a circular crack. Acta Mech., 126:169-187.

[63] Karapetian, E., Sevostianov, I., Kachanov, M., 2000. Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading. Arch. Appl. Mech., 70:201-229.

[64] Karapetian, E., Kachanov, M., Sevostianov, I., 2002. The principle of correspondence between elastic and piezoelectric problems. Arch. Appl. Mech., 72:564-587.

[65] Kogan, L., Hui, C.Y., Molkov, V., 1996. Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezoelectric material. Int. J. Solids Struct., 33:2719-2737.

[66] Muskhelishvili, N.I., 1953. Singular Integral Equations. Noordhoff, Groningen.

[67] Podil’chuk, Y.N., Sokolovskii, Y.I., 1994. Thermostress in an infinite transversally isotropic medium with an internal elliptical crack. Int. Appl. Mech., 30:834-840.

[68] Popova, M., Gorbatikh, L., 2004. On partial sliding along a planar crack: The case of a circular sliding zone. Arch. Appl. Mech., 73:580-590.

[69] Sneddon, I.N., 1966. Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Company, Amsterdam.

[70] Sneddon, I.N., Lowengrub, M., 1969. Crack Problems in the Classical Theory of Elasticity. John Wiley, New York.

[71] Tsai, Y.M., 1983. Thermal stress in a transversely isotropic medium containing a penny-shaped crack. J. Appl. Mech., 50:24-28.

[72] Wang, B., 1992. Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. Int. J. Eng. Sci., 30:781-791.

[73] Wang, M.Z., 2002. Advanced Theory of Elasticity. Peking University Press, Beijing (in Chinese).

[74] Wang, Z.K., Zheng, B.L., 1995. The general solution of three-dimensional problems in piezoelectric media. Int. J. Solids Struct., 31:105-115.

[75] Xiao, Z.M., Fan, H., Zhang, T.L., 1995. Stress intensity factors of two skew-parallel penny-shaped cracks in a 3-D transversely isotropic solid. Mech. Mater., 20:261-272.

[76] Yong, Z., Hanson, M.T., 1992. Stress intensity factors for annular cracks in inhomogeneous isotropic materials. Int. J. Solids Struct., 29:1033-1050.

[77] Yong, Z., Hanson, M.T., 1994a. A circular crack system in an infinite elastic medium under arbitrary normal loads. J. Appl. Mech., 61:582-588.

[78] Yong, Z., Hanson, M.T., 1994b. Three-dimensional crack and contact problems with a general geometric configuration. Int. J. Solids Struct., 31:215-239.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE