×

Fracture dynamics with allowance for crack edge contact interaction. (English) Zbl 1241.74032

Summary: In this review article general results are presented concerning problems in the fracture dynamics of elastic bodies with allowance for unilateral crack edge contact interaction with friction. A formulation has been made of the elastodynamic contact problem with unilateral restrictions for bodies with cracks under arbitrary dynamic loading. A specific case of harmonic loading important to these applications has also been considered. The mathematical aspects of the elastodynamics problem for bodies with cracks and with unilateral restrictions in the form of inequalities on the crack edges have been considered in brief. A variational formulation of the problem has been given. Boundary variational inequalities and boundary functional have been derived. The boundary integral equations (BIE) method in a Laplace transform domain has been used as a solution for the elastodynamic problem for bodies with cracks. Singularities of the kernels in these integral equations have been studied. Two regularization methods of the potentials with “strongly” singular kernels have been considered. The first is based on its transformation into integro-differentional equations. The second consists of the utilization of the BIE with hypersingular integrals, which are considered in the sense of a finite part, according to Hadamard. An algorithm for the solution of the elastodynamic unilateral contact problem for bodies with cracks has been elaborated. The algorithm is based on finding a saddle point of a sub-differentional boundary functional. It has been shown that the algorithm may be considered as a compressive operator, which acts in corresponding functional spaces. This means that the algorithm is convergent. Numerical methods have been elaborated for the solution to elastodynamic contact problems with unilateral restrictions and friction for bodies with cracks. The problem has been solved, for plane harmonic tension-compression wave propagation in a plane with one and two colinear finite length cracks and with allowance for unilateral contact interaction of the crack edges. Dependence of the solution accuracy on the approximation of coordinates and time, and also of numbers of terms in the expansion of the stress-strain state components into Fourier series, has been investigated. Numerical results have also been presented. Quantitative and qualitative effects caused by contact interaction of the crack edges have been investigated. This review contains 170 references.

MSC:

74R10 Brittle fracture
76M15 Boundary element methods applied to problems in fluid mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agranovitch M.S., Uspehi Mat. Nauk. 19 (3) pp 53– (1964)
[2] DOI: 10.1115/1.3101690 · doi:10.1115/1.3101690
[3] Beskos D.E, Applied Mechanics Reviews, 40( 1) ( pp 1– (1987)
[4] DOI: 10.1115/1.3101695 · doi:10.1115/1.3101695
[5] DOI: 10.1115/1.3098922 · doi:10.1115/1.3098922
[6] DOI: 10.1016/0022-5096(60)90006-5 · Zbl 0087.17702 · doi:10.1016/0022-5096(60)90006-5
[7] DOI: 10.1002/nme.1620100206 · Zbl 0322.73016 · doi:10.1002/nme.1620100206
[8] DOI: 10.1016/0022-247X(68)90171-6 · Zbl 0167.16301 · doi:10.1016/0022-247X(68)90171-6
[9] DOI: 10.1016/0021-9991(79)90025-1 · Zbl 0416.65077 · doi:10.1016/0021-9991(79)90025-1
[10] Durbin F, Computer Journal 17 pp 371– (1974)
[11] Goeleven D., Methods & Applications, 29( 1) ( pp 9– (1997)
[12] DOI: 10.1002/(SICI)1099-1476(199704)20:6<547::AID-MMA869>3.0.CO;2-G · Zbl 0866.49019 · doi:10.1002/(SICI)1099-1476(199704)20:6<547::AID-MMA869>3.0.CO;2-G
[13] DOI: 10.1002/zamm.19970770703 · Zbl 0920.70013 · doi:10.1002/zamm.19970770703
[14] DOI: 10.1002/nme.1620290603 · Zbl 0717.73081 · doi:10.1002/nme.1620290603
[15] Guz A.N, International Applied Mechanics 34 (12) pp 3– (1998)
[16] DOI: 10.1007/BF02682056 · doi:10.1007/BF02682056
[17] Guz A.N, Int. Applied Mechanics 35 (2) pp 3– (1999)
[18] DOI: 10.1007/BF02682116 · doi:10.1007/BF02682116
[19] DOI: 10.1007/BF02682174 · doi:10.1007/BF02682174
[20] Guz A.N., Dokladi Academii Nauk USSR 318 (2) pp 304– (1991)
[21] Guz A.N., Dokladi Academii Nauk USSR 321 (2) pp 278– (1991)
[22] DOI: 10.1007/BF00847122 · Zbl 0799.73054 · doi:10.1007/BF00847122
[23] DOI: 10.1007/BF00847134 · doi:10.1007/BF00847134
[24] Guz A.N., Material Science, 32( 1) ( pp 38– (1996)
[25] DOI: 10.1007/BF01295569 · Zbl 0499.73112 · doi:10.1007/BF01295569
[26] Ioakinidis N.I, International Journal of Fracture 38 pp 75– (1988)
[27] Kantor B.Ya., Mehanika Tverdogo Tela 5 pp 80– (1991)
[28] Kaya A.C., Quarterly of Applied Mathematics 45 (1) pp 105– (1987)
[29] DOI: 10.1016/0021-8928(80)90178-1 · Zbl 0449.73122 · doi:10.1016/0021-8928(80)90178-1
[30] Krishnasamy G., Chap. 7 pp 207– (1992)
[31] DOI: 10.1007/BF01436592 · Zbl 0306.65010 · doi:10.1007/BF01436592
[32] DOI: 10.1016/0020-7225(70)90003-0 · Zbl 0213.27502 · doi:10.1016/0020-7225(70)90003-0
[33] Manolis G.D, Int. J. Eng. Science 19 (1) pp 73– (1983)
[34] DOI: 10.1016/0955-7997(91)90013-J · doi:10.1016/0955-7997(91)90013-J
[35] DOI: 10.1016/0955-7997(93)90034-I · doi:10.1016/0955-7997(93)90034-I
[36] Morse P.M., Part 1 pp 2– (1953)
[37] DOI: 10.1007/BF01395957 · Zbl 0442.65016 · doi:10.1007/BF01395957
[38] Papoulis A, Quarterly of Applied Mathematics 14 pp 405– (1957)
[39] DOI: 10.1016/0771-050X(75)90029-7 · Zbl 0302.65092 · doi:10.1016/0771-050X(75)90029-7
[40] Polizzotto C., Tanaka M. and Cruse T.A.) 1988 pp 13–
[41] Sih G.C., Quarterly of Applied Mathematics 27 (2) pp 193– (1969)
[42] DOI: 10.1016/0045-7949(86)90191-4 · Zbl 0595.73087 · doi:10.1016/0045-7949(86)90191-4
[43] DOI: 10.1115/1.3111062 · doi:10.1115/1.3111062
[44] Telega Yu.I, Uspehi Mehaniki 10 (2) pp 3– (1987)
[45] DOI: 10.1002/nme.1620350809 · Zbl 0767.73089 · doi:10.1002/nme.1620350809
[46] DOI: 10.1016/0020-7683(93)90078-L · Zbl 0773.73084 · doi:10.1016/0020-7683(93)90078-L
[47] DOI: 10.1007/BF02259907 · Zbl 0504.65011 · doi:10.1007/BF02259907
[48] Volevich L.R., Uspehi Matematicheskih Nauk 20 (1) pp 3– (1965)
[49] DOI: 10.1007/BF02384079 · Zbl 0725.73091 · doi:10.1007/BF02384079
[50] Wheeler L.T., Archive for Ration Mechanics and Analysis 31 (1) pp 51– (1968)
[51] Yoffe E, Philosophical Magazine 42 (330) pp 739– (1951)
[52] DOI: 10.1016/0021-8928(89)90111-1 · Zbl 0727.73067 · doi:10.1016/0021-8928(89)90111-1
[53] Zozulya V.V, Mashinostroenie 1 pp 24– (1990)
[54] Zozulya V.V, Mathamika Techicheckie Nauki 3 pp 53– (1990)
[55] Zozulya V.V, Mathamika Techicheckie Nauki 2 pp 19– (1991)
[56] DOI: 10.1007/BF01301505 · Zbl 0793.73082 · doi:10.1007/BF01301505
[57] DOI: 10.1007/BF00847331 · Zbl 0800.73177 · doi:10.1007/BF00847331
[58] DOI: 10.1007/BF00847208 · doi:10.1007/BF00847208
[59] Zozulya V.V., Mehanika Tverdogo Tela 2 pp 160– (1992)
[60] Zozulya V.V, Dokladi Akademii Nauk Ukrainy 2 pp 38– (1992)
[61] DOI: 10.1007/BF00848206 · doi:10.1007/BF00848206
[62] Zozulya V.V, Dokladi Akademii Nauk Ukrainy 3 pp 38– (1992)
[63] DOI: 10.1007/BF02682152 · doi:10.1007/BF02682152
[64] DOI: 10.1080/02533839.1999.9670512 · doi:10.1080/02533839.1999.9670512
[65] DOI: 10.1016/S0955-7997(00)00029-1 · Zbl 0982.74080 · doi:10.1016/S0955-7997(00)00029-1
[66] Zozulya V.V., International Applied Mechanics 34 (6) pp 544– (1988)
[67] DOI: 10.1007/BF00846829 · Zbl 0855.73070 · doi:10.1007/BF00846829
[68] DOI: 10.1007/BF02681961 · doi:10.1007/BF02681961
[69] DOI: 10.1080/02533839.2000.9670551 · doi:10.1080/02533839.2000.9670551
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.