×

BIE fracture mechanics analysis: 25 years of developments. (English) Zbl 0946.74073

From the introduction: We review the capabilities of the boundary integral equation (BIE) method for problems in fracture mechanics. The problem class will be limited to static problems of elastic and elastoplastic fracture. The paper draws on the extensive literature that has been developed over the past twenty-five years. Fracture mechanics problems have provided one of the most important applications of BIE formulations in solid mechanics and is one of the principal areas of application of BIE methods. In particular, the paper focuses on the special role played by the Somigliana stress identity in providing algorithms and analytical results for fracture mechanics analysis that are not possible when using the finite element method. Finally, we also identify special problems associated with BIE modeling of cracks, and various strategies that have been developed to successfully treat these problems.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74R10 Brittle fracture
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74R20 Anelastic fracture and damage
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aliabadi, M. H.; Rooke, D. P.; Cartwright, D. J. 1987: An improved boundary element formulation for calculating stress intensity factors: application to aerospace structures, J. Strain Anal. 22: 203-207 · doi:10.1243/03093247V224203
[2] Ang, W. T. 1986: A boundary integral solution for the problem of multiple interacting cracks in an elastic media, Int. J. Frac., 31: 259-270 · doi:10.1007/BF00044049
[3] Annigeri, B. S.; Cleary, M. P. 1984: Surface integral finite element hybrid method for fracture mechanics, Intl. J. Numer. Methods Engrg., 20: 869-885 · Zbl 0528.73074 · doi:10.1002/nme.1620200507
[4] Ayres, D. J. 1970: A numerical procedure for calculating stress and deformation near a slit in a three dimensional elastic plastic solid, Engrg. Fract. Mechs., 2: 87-106 · doi:10.1016/0013-7944(70)90015-9
[5] Barsoum, R. S. 1976: On the use of isoparametric finite elements in linear fracture mechanics, Int. J. Numer. Math. Engrg., 10: 25-37 · Zbl 0321.73067 · doi:10.1002/nme.1620100103
[6] Bentham, J. P. 1977: State of stress at the vertex of a quarter-infinite crack in a half space, Int. J. Solids Struct., 13: 479-492 · Zbl 0364.73089 · doi:10.1016/0020-7683(77)90042-7
[7] Blandford, G. E.; Ingraffea, A. R.; Liggett, J. A. 1981: Two dimensional stress intensity factor computations using the boundary element method, Int. J. Numer. Meth. Engrg., 17: 387-404 · Zbl 0463.73082 · doi:10.1002/nme.1620170308
[8] Bui, H. D. 1977: An integral equations method for solving the problem of a plane crack or arbitrary shape, J. Mechs. Phys. Sol., 25: 29-39 · Zbl 0355.73074 · doi:10.1016/0022-5096(77)90018-7
[9] Bui, H. D. 1978: Some remarks about the formulation of three-dimensional thermoelastoplastic problems by integral equations, Int. J. Solids Struct., 14: 935-939 · Zbl 0384.73008 · doi:10.1016/0020-7683(78)90069-0
[10] Grouch, S. L. 1976: Solution of plane elasticity problems by the displacement discontinuity method, Int. J. Numer. Meth. Engrg., 10: 301-343 · Zbl 0322.73016 · doi:10.1002/nme.1620100206
[11] Crouch, S. L.; Starfield, A. M. 1983: Boundary Element Methods in Solid Mechanics, George Allen & Unwin, London · Zbl 0528.73083
[12] Cruse, T. A. 1969: Numerical solutions in three-dimensional elastostatics, Intl. J. Solids Struct., 5: 1259-1274 · Zbl 0181.52404 · doi:10.1016/0020-7683(69)90071-7
[13] Cruse, T. A. 1970: Lateral constraint in a cracked, three-dimensional elastic body, Int. J. Frac. Mechs. 6: 326-328
[14] Cruse, T. A.; VanBuren, W. 1971: Three dimensional elastic stress analysis of a fracture specimen with an edge crack, Intl. J. of Fract. Mechs., 7: 1, 1-15
[15] Cruse, T. A. 1972: Numerical evaluation of elastic stress intensity factors by the boundary-integral equation method, in The Surface Crack: Physical Problems and Computational Solutions, ed. J. L. Swedlow, American Society of Mechanical Engineers, 153-170
[16] Cruse, T. A. 1973: Application of the boundary-integral equation method to three dimensional stress analysis, Comp. & Struct., 3: 509-527 · doi:10.1016/0045-7949(73)90094-1
[17] Cruse, T. A. 1974: An improved boundary-integral equation method for three dimensional elastic stress analysis, Comp. & Struct., 4: 741-754 · doi:10.1016/0045-7949(74)90042-X
[18] Cruse, T. A. 1975: Boundary-integral equation method for three dimensional elastic fracture mechanics analysis, U.S. Air Force Report AFOSR-TR-75-0813, Accession No. ADA011660
[19] Cruse, T. A.; Besuner, P. M., 1975: Residual life prediction for surface cracks in complex structural details, AIAA Journal of Aircraft, 12: 369-375 · doi:10.2514/3.44458
[20] Cruse, T. A.; Meyers, G. J., 1977: Three dimensional fracture mechanics analysis, ASCE Journal of the Structural Division, 103: 309-320
[21] Cruse, T. A.; Wilson, R. B. 1978a: Boundary-integral equation method for elastic fracture mechanics analysis, U.S. Air Force Report AFOSR-TR-78-0355, Accession No. ADA051992 · Zbl 0377.73054
[22] Cruse, T. A.; Wilson, R. B., 1978b: Advanced applications of the boundary-integral equation method. Nuclear Engrg. Des., 46: 233-234
[23] Cruse, T. A. 1978: Two-dimensional BIE fracture mechanics analysis, Appl. Math. Modeling, 2: 287-293 · Zbl 0436.73110 · doi:10.1016/0307-904X(78)90023-9
[24] Cruse, T. A.; Polch, E. Z. 1986a: Elastoplastic BIE analysis of cracked plates and related problems, Parts I and II, Int. J. Numer. Meth. Engrg., 23: Part I, 429-437, Part II, 439-452 · Zbl 0583.73072 · doi:10.1002/nme.1620230308
[25] Cruse, T. A.; Polch, E. Z., 1986b. Application of an elastoplastic boundary-element method to some fracture mechanics problems, Engrg. Frac. Mechs., 23: 1085-1096 · Zbl 0583.73072 · doi:10.1016/0013-7944(86)90149-9
[26] Cruse, T. A. 1987: Fracture mechanics, in Boundary Element Methods in Mechanics, ed. D.E. Beskos, Elsevier Science Publishers B.V., The Netherlands: pp. 333-365
[27] Cruse, T. A. 1988a: Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Amsterdam · Zbl 0648.73039
[28] Cruse, T. A. 1988b: Three dimensional elastic surface cracks, in Fracture mechanics: Nineteenth Symposium, ASTM STP 969, ed. by T.A. Cruse, American Society for Testing and Materials, Philadelphia: 19-42
[29] Cruse, T. A.; Raveendra, S. T., 1988a: A general solution procedure for fracture mechanics weight function evaluation based on the boundary element method, Comp. Mechs., 3: 157-166 · Zbl 0631.73081 · doi:10.1007/BF00297442
[30] Cruse, T. A.; Raveendra, S. T. 1988b: A comparison of long and short crack elastoplastic response using the boundary element method, Engrg. Frac. Mechs., 30: 59-75 · Zbl 0631.73081 · doi:10.1016/0013-7944(88)90255-X
[31] Cruse, T. A.; Novati, G. 1992: Traction BIE formulations and applications to nonplaner and multiple cracks, Fracture Mechanics: Twenty-Second Symposium (Vol. II), ASTM STP 1131, ed. S.N. Atluri et al., American Society for Testing and Materials, Philadelphia: 314-332
[32] Cruse, T. A.; Suwito, W. 1993: On the Somigliana stress identity in elasticity, Comp. Mechs., 11: 1-10 · Zbl 0763.73061 · doi:10.1007/BF00370069
[33] Cruse, T. A.; Richardson, J. D. 1996: The non-singular Somigliana stress-BIE, Int. J. Numer. Meth. Engrg., in press · Zbl 0886.73005
[34] Eshelby, J. D.; Reed, W. T.; Shockley, W., 1957: Anisotropic elasticity with applications to dislocation theory, Acta Metal., 1: 251-259 · doi:10.1016/0001-6160(53)90099-6
[35] Gangming, L.; Youngyuan, Z., 1988: Application of boundary element method with singular and isoparametric elements in three dimensional crack problems, Engrg. Frac. Mechs., 29: 97-106 · doi:10.1016/0013-7944(88)90010-0
[36] Green, A. E.; Sneddon, I. N., 1950: The stress distribution in the neighborhood of a flat elliptical crack in an elastic solid, Proc. Cambridge Phil. Soc., 46: 159-163 · Zbl 0039.20101 · doi:10.1017/S0305004100025585
[37] Griffith, A. A. 1920: The phenomenon of rupture and flow in solids, Phil. Trans. R. Soc., A, 221: 163-198 · doi:10.1098/rsta.1921.0006
[38] Guidera, J. T.; Lardner, R. W., 1975: Penny-shaped cracks, J. Elas., 5: 59-73 · Zbl 0312.73117 · doi:10.1007/BF01389258
[39] Krishnasamy, G.; Rizzo, F. J.; Rudolphi, T. J., 1992: Continuity requirements for density functions in the boundary integral equation method, Comp. Mechs., 9: pp. 267-284 · Zbl 0755.65108 · doi:10.1007/BF00370035
[40] Hack, J. E., Chan, K. S.; Cardinal, J. W., 1985: The prediction of the crack opening behavior of part-through fatigue cracks under the influence of surface residual stresses, Engrg. Fract. Mechs., 21: 75-83 · doi:10.1016/0013-7944(85)90055-4
[41] Heliot, J.; Labbens, R. C. 1979: Results for benchmark problem 1: the surface flaw, Int. J. Fract. 15: R197-R202 · doi:10.1007/BF00019927
[42] Huang, Q.; Cruse, T. A. 1994: On the nonsingular traction-BIE in elasticity, Int. J. Numer. Meth. Engrg., 37: 2041-2072 · Zbl 0832.73076 · doi:10.1002/nme.1620371204
[43] Inglis, C. E., 1913: Stresses in a plate due to the presence of cracks and sharp corners, Proceedings of the Institute of Naval Architects, 60: 219-230
[44] Irwin, G. R. 1957: Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mechs., 24: 361-364
[45] Kim, J.-W. 1985: A contour integral computation of stress intensity factors in the cracked orthotropic elastic plates, Engrg. Fract. Mechs., 21: 353-364 · doi:10.1016/0013-7944(85)90023-2
[46] Lachat, J. C.; Watson, J. O. 1976: Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastoplastics, Int. J. Numer. Meth. Engrg., 10: 991-1005 · Zbl 0332.73022 · doi:10.1002/nme.1620100503
[47] Li, R.; Chudnovsky, A. 1994: The stress intensity factor Green’s function for a crack interacting with a circular inclusion, Int. J. Fract., 67: 169-177 · doi:10.1007/BF00019602
[48] Martin, P. A. 1982: The discontinuity in the elastostatic displacement vector across a penny-shaped crack under arbitrary loads, J. Elas., 12: 201-218 · Zbl 0512.73089 · doi:10.1007/BF00042216
[49] Melnikov, Yu. A. 1995: Green’s Functions in Applied Mechanics, Computational Mechanics Publications, Southampton UK · Zbl 0898.73001
[50] Mukherjee, S., 1982: Boundary Element Methods in Creep and Fracture, Applied Science, Essex UK · Zbl 0534.73070
[51] Polch, E. Z.; Cruse, T. A.; Huang, C.-J. 1987: Traction BIE solutions forflat cracks, Comp. Mechs., 2: 253-267 · Zbl 0616.73093 · doi:10.1007/BF00296420
[52] Putot, C. J., 1980: Une nouvelle methode d’equations integrales pour certains problems de fissures planes, Ph.D. Thesis, University Pierre et Marie Curie, Paris VI
[53] Raveendra, S. T.; Cruse, T. A. 1989: BEM analysis of problems of fracture mechanics, in Industrial Applications of Boundary Element Methods, ed. P. K. Banerjee; R. B. Wilson, Elsevier Applied Science, London, 186-204
[54] Raju, I. S.; Newman, Jr., J. C. 1977: Three dimensional finite element analysis of finite thickness fracture specimens, NASA Technical Note TN D-8414, Washington, D. C.
[55] Rudolphi, T. J.; Koo, L. S. 1985: Boundary element solutions of multiple, interacting crack problems in plane elastic media, Engrg. Anal., 2: 211-216 · doi:10.1016/0264-682X(85)90034-6
[56] Schmitz, H.; Volk, K.; Wendland, W. 1993: Three-dimensional singularities of elastic fields near vertices, Numer. Meth. P. Diff. Eqtns., 9: 323-337 · Zbl 0771.73014 · doi:10.1002/num.1690090309
[57] Sinclair, J. E.; Hirth, J. P. 1975: Two dimensional elastic Green function for a cracked anisotropic body, J. Phys. F Metal Phys., 5: 236-246 · doi:10.1088/0305-4608/5/2/007
[58] Snyder, M. D.; Cruse, T. A. 1975: Boundary-integral equation analysis of cracked anisotropic plates, Intl. J. of Fract. Mechs., 11: 2, 315-328
[59] Stern, M.; Becker, E. B.; Dunham, R. S. 1976: A contour integral computation of mixed-mode stress intensity factors, Int. J. Fract., 12: 359-368
[60] Swedlow, J. L.; Cruse, T. A. 1971: Formulation of the boundary integral equation for three-dimensional elasto-plastic flow, Int. J. Solids Struct., 7: 1673-1683 · Zbl 0228.73040 · doi:10.1016/0020-7683(71)90006-0
[61] Tan, C. L.; Fenner, R. T. 1979: Elastic fracture mechanics analysis by the boundary integral equation method, Proc. R. Soc. Lond. A, 369: 243-260 · Zbl 0441.73108 · doi:10.1098/rspa.1979.0162
[62] Tanaka, M.; Itoh, H. 1987: New crack elements for boundary element analysis of elastostatics considering arbitrary stress singularities, Appl. Math. Model., 11: 357-363 · Zbl 0625.73116 · doi:10.1016/0307-904X(87)90030-8
[63] Telles, J. C. F. 1983: The Boundary Element Method Applied to Inelastic Problems, Vol. 1 in the series Lecture Notes in Engineering, ed. C. Brebbia and S. A. Orzag, Springer-Verlag, Berlin · Zbl 0533.73076
[64] Tracey, D. M. 1971: Finite elements for determination of crack tip elastic stress intensity factors, Engrg. Fract. Mechs., 3: 255-265 · doi:10.1016/0013-7944(71)90036-1
[65] Williams, M. L. 1952: Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mechs., 19: 526-528
[66] Weaver, J. 1977: Three dimensional crack analysis, Intl. J. Soc. Struct., 13: 321-330 · Zbl 0373.73093 · doi:10.1016/0020-7683(77)90016-6
[67] Weeën, F. van der, 1983: Mixed mode fracture analysis of rectilinear anisotropic plates using singular boundary elements, Comp. & Struct., 17: 469-474 · Zbl 0511.73113
[68] Xanthis, L. S.; Bernal, M. J. M.; Atkinson, C. 1981: The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method, Comp. Meth. Appl. Mechs. Engrg., 26: 285-304 · Zbl 0461.73066 · doi:10.1016/0045-7825(81)90118-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.