Elastic complex analysis and its applications in fracture mechanics

International Journal of Solids and Structures

Volumn 37, Issue 28, 2000, Pages 3873-3895

  Aparicio, N D ^a  

^a OXFORD BROOKES UNIVERSITY   (United Kingdom)

Author keywords

Boundary elements; Complex analysis; Fracture mechanics; Muskhelisavili potentials; Path independent integrals; Plane elasticity; Weight functions

Indexed keywords

BOUNDARY ELEMENT METHOD; DIFFERENTIATION (CALCULUS); EQUATIONS OF MOTION; FRACTURE MECHANICS; FUNCTIONS; INTEGRATION;

MUSKHELISAVILI POTENTIALS; WEIGHT FUNCTIONS;

ELASTICITY;

EID: 0033906686     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(99)00230-9     Document Type: Article

References (24)

1. Aparicio, N.D., Pidcock, M.K., 1996. The boundary inverse problem for the Laplace equation in two dimensions. Inverse Problems 12, 565-577.
2. Aparicio, N.D., Atkinson, C., 1997. Ancillary solutions for curved crack stress analysis. Proc. R. Soc. Lond A453, 2207-2228.
3. Atkinson, C., Aparicio, N.D., 1994. An inverse problem method for antiplane crack detection in elastic materials. Proc. R. Soc. Lond A445, 637-652.
4. Atkinson, C., Aparicio, N.D., 1999. Fracture detection problems: applications and limitations of the energy momentum tensor and related invariants. Int. J. Solids Struct 36, 4889-4899.
5. Chang, C., Mear, M.E., 1995. A boundary element method for two dimensional linear elastic fracture analysis. Int. J. Fract 74, 219-251.
6. Chen, Y.Z., 1993. New Fredholm integral-equation for multiple crack problem in plane elasticity and antiplane elasticity. Int. J. Fract 64, 63-77.
7. Chen, Y.Z., Cheung, Y.K., 1994. A new boundary integral-equation for notch problem of plane elasticity. Int. J. Fract 66, 91-97.
8. Dong, X.Y., 1994. Representation of stress intensity factors by path-integrals of the first stress invariant or antiplane displacement for general 2-dimensional static problems. Int. J. Fract 68, 127-140.
9. Edelen, D.G.B., 1981. Aspects of variational arguments in the theory of elasticity: fact and folklore. Int. J. Solids Struct 17, 729-740.
10. Eshelby, J.D., 1956. The continuum theory of lattice deffects. In: Seitz, F., Turnbull, D. (Eds.), Solid State Physics, 3. Academic Press, New York, pp. 79-144.
11. Eshelby, J.D., 1975. The elastic energy-momentum tensor. Journal of Elasticity 5, 321-335.
12. Freund, L.B., 1990. Dynamic Fracture Mechanics. Cambridge University Press, Cambridge, UK.
13. Günther, W., 1962. Abh. Braunschw. Wiss. Ges 14, 54.
14. Ioakimidis, N.I., Anastasselou, E.G., 1993. Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity. Acta Mechanica 98, 99-106.
15. Knowles, J.K., Sternberg, E., 1972. On a class of conservation laws in linearized and finite elastostatics. Arch. Rational Mech. Anal 44, 187-211.
16. MacGregor, C.W., 1935. The potential function method for the solution of two-dimensional stress problems. Transactions of the American Mathematical Society 38, 177-186.
17. Muskhelishvili, N.I., 1958. Singular Integral Equations. Wolters-Noordhoff, Groningen, The Netherlands.
18. Muskhelishvili, N.I., 1963. Some Basic Problems of the Mathematical Theory of Elasticity, 4th edn. Wolters-Noordhoff, Groningen, The Netherlands.
19. Noether, E., 1918. Invariante Variationsprobleme. Math.-Physik. K1 2, 235-257.
20. Olver, P.J., 1984a. Conservation laws in elasticity. Part I: general results. Arch. Rational Mech. Anal 85, 111-129.
21. Olver, P.J., 1984b. Conservation laws in elasticity. Part II: linear homogeneus isotropic elastostatics. Arch. Rational Mech. Anal 85, 131-160.
22. Rice, J.R., 1968. A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech 35, 379-386.
23. Tsamasphyros, G.J., Theocaris, P.S., 1982. A new concept of path-independent integrals for plane elasticity. J. Elast 12, 265-280.
24. Westergaard, H.M., 1939. Bearing pressures and cracks. ASME Journal of Applied Mechanics 6, A49-A53.