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Viscoelastic crack analysis by the boundary integral equation method

Viskoelastische Rißanalyse durch Randintegralgleichungen

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Summary

The linear viscoelastic three-dimensional crack problem is analyzed by combining the correspondence principle and the boundary integral equation method. In a general crack analysis the usual boundary integral equations lead to a nonunique formulation of the problem, because they do not involve information about the loading on the crack surface. Here, the boundary integro-differential equations are applied to the numerical calculation of the crack opening displacement of a penny-shaped crack in an infinite linear viscoelastic body. Moreover, the influence of several parameters of the three-parameter viscoelastic model on the crack opening displacement and the incubation time is shown.

Übersicht

Das linear viskoelastisch räumliche Rißproblem wird mit Hilfe einer Kombination von Korrespondenzprinzip und Randintegralgleichungsverfahren gelöst. In einer allgemeinen Rißanalyse führen die üblichen Randintegrale zu einer nicht eindeutigen Formulierung dieses Problems, weil die Angaben über Belastung und Rißoberfläche fehlen. Das Randintegralgleichungsverfahren wird für die numerische Berechnung der Rißerweiterung eines münzförmigen Risses in einem unendlich linear viskoelastischen Körper angewendet. Weiterhin wird der Einfluß von verschiedenen Parametern des räumlich viskoelastischen Modells auf die Rißerweiterung und die Inkubationszeit gezeigt.

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References

  1. Irwin, G. R.: Fracture mechanics, structural mechanics. Proc. 1st Symposium on Naval Structura Mech. 1960, 557–591

  2. Wnuk, M. P.; Knauss, W. G.: Delayed fracture in viscoelastoplastic solids. Int. J. Solids Struct. 6 (1970) 995–1010

    Google Scholar 

  3. Schapery, R. A.: A theory of crack initiation and growth in viscoelastic media. Int. J. Fract. 11 (1975) 141–159

    Google Scholar 

  4. Kaminskij, A. A.: Mechanika razruschenia vjazko-uprugich tel, Kiev 1980 (in Russian)

  5. Graham, G. A. C.: The correspondence principle of linear viscoelasticity theory for mixed boundary value problems involving time dependent boundary regions. Q. Appl. Math. 26 (1968) 167–174

    Google Scholar 

  6. Graham, G. A. C.: The solution of mixed boundary value problems that involve time-dependent boundary regions for viscoelastic materials with one relaxation function. Acta Mech. 8 (1969) 188–204

    Google Scholar 

  7. Rabotnov, J. N.: Polzuchest elementov konstrukcij. Moskva: Nauka 1966 (in Russian)

    Google Scholar 

  8. Boley, B. A.; Weiner, J. H.: Theory of thermal stresses. New York: Wiley and Sons 1960

    Google Scholar 

  9. Brebbia, C. A.; Walker, S.: Boundary element techniques in engineering. London: Newnes-Butterworths 1980

    Google Scholar 

  10. Sládek, V.; Sládek, J.: Three dimensional crack analysis for an anisotropic body. Appl. Math. Modelling 6 (1982) 374–380

    Google Scholar 

  11. Sládek, J.; Sládek, V.: Boundary element method in fracture mechanics. Acta technica ČSAV 27 (1982) 718–732

    Google Scholar 

  12. Sládek, V.; Sládek, J.: Transient elastodynamic three-dimensional problems in cracked bodies. Appl. Math. Modelling 8 (1984) 2–10

    Google Scholar 

  13. Rizzo, F. J.; Shippy, D. J.: An application of the correspondence principle of linear viscoelasticity. SIAM J. Appl. Math. 21 (1971) 321–330

    Google Scholar 

  14. Kusama, T.; Mitsui, Y.: Boundary element method applied to linear viscoelastic analysis. Appl. Math. Modelling 6 (1982) 285–290

    Google Scholar 

  15. Sládek, J.; Sládek, V.: Dynamic stress intensity factor studied by boundary integro-differential equations. (to be published)

  16. Schapery, R. A.: Approximate methods of transform inversion for viscoelastic stress analysis. Proc. 4th US. Nat. Congr. Appl. Mech. 1962, 1075–1085

  17. Kusama, T.; Mitsui, Y.; Yoshida, S.: Linear viscoelastic analysis by using numerical inversion of the Laplace transform. Trans. JSCE 11 (1979) 113–115

    Google Scholar 

  18. Lichardus, S.; Sumec, J.: Modelling of viscoelastic properties of reinforced concrete. Proc. of IABSE/ CEB/ASCE/RILEM Colloquium, Delft 1981, 327–334

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Authors and Affiliations

  1. Institute of Construction and Architecture of Slovak Academy of Sciences, 842 20, Bratislava, Czechoslovakia

    J. Sládek,  J. Sumec &  V. Sládek

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  1. J. Sládek
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  2. J. Sumec
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  3. V. Sládek
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Sládek, J., Sumec, J. & Sládek, V. Viscoelastic crack analysis by the boundary integral equation method. Ing. arch 54, 275–282 (1984). https://doi.org/10.1007/BF00532553

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