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Reciprocity in fracture and defect mechanics

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Abstract

For defects in solids, when displaced within the material, reciprocity relations have been established recently similar to the theorems attributed to Betti and Maxwell. These theorems are applied to crack- and defect-interaction problems.

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References

  • Barber JR (2002). Elasticity, 2nd edn. Kluwer, Dordrecht

    Google Scholar 

  • Budiansky B and Rice J (1973). Conservation laws and energy-release rates. ASME J Appl Mech 40: 201–203

    Google Scholar 

  • Erdogan F (1962) On the stress distribution in plates with collinear cuts under arbitrary loads. In: Proceedings of the Fourth U.S. National Congress of Applied Mechanics. ASME 1:547–553

  • Gross D (1982). Spannungsintensitätsfaktoren von Rißsystemen. Ing Arch 51: 301–310

    Article  Google Scholar 

  • Günther W (1962). Über einige Randintegrale der Elastomechanik. Abh Braunschw Wiss Ges 14: 53–72

    Google Scholar 

  • Gurson AL (1977). Continuum theory of ductile rupture by void nucleation and growth. Part I—yield criteria and flow rules for porous ductile media. J Eng Mater Tech 99: 2–15

    Google Scholar 

  • Gurtin ME (2000). Configurational forces as basic concepts of continuum physics. Springer, New York

    Google Scholar 

  • Herrmann G and Kienzler R (2007a). Reciprocity relations in Eshelbian mechanics. Mech Res Commun 34: 338–343

    Article  Google Scholar 

  • Herrmann G, Kienzler R (2007b) A reciprocity relation couples Newtonian and Eshelbian Mechanics. ASME J Appl Mech (in press)

  • Kienzler R and Herrmann G (2000). Mechanics in material space. Springer, Berlin

    Google Scholar 

  • Kienzler R, Herrmann G (2007) Nonlinear and linearized reciprocity relations in structural configurational mechanics. Acta Mech doi: 1007/s00707-007-0457-5

    Google Scholar 

  • Kienzler R and Kordisch H (1990). Calculation of J 1 and J 2, using the L and M integral. Int J Fract 43: 213–225

    Article  Google Scholar 

  • Knowles JK and Sternberg E (1972). On a class of conservation laws in linearized and finite elastostatics. Arch Rat Mech Anal 44: 187–211

    Article  Google Scholar 

  • Marguerre K (1962) Elasticity, basic concepts. In: Flügge W Handbook of engineering mechanics. McGraw-Hill, New York

  • Maugin GA (1993). Material inhomogeneities in elasticity. Chapman & Hall, London

    Google Scholar 

  • Panasyuk MP, Savruk MP and Datsyshyn AP (1977). A general method of solution of two-dimensional problems in the theory of cracks. Eng Fract Mech 9: 481–497

    Article  Google Scholar 

  • Rice JR (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME J Appl Mech 27: 379–386

    Google Scholar 

  • Rohde L and Kienzler R (2005). Numerical computation and analytical estimation of stress-intensity factors for strips with multiple edge cracks. Arch Appl Mech 74: 846–852

    Article  Google Scholar 

  • Rohde L, Kienzler R and Herrmann G (2005). On a new method for calculating stress-intensity factors of multiple edge cracks. Phil Mag 85: 4231–4244

    Article  CAS  Google Scholar 

  • Schweins G (1849). Fliehmomente oder die Summe (xX + yY) bei Kräften in der Ebene und (xX + yYzZ) bei Kräften im Raume. Crelles J Reine Angew Math 38: 77–88

    Google Scholar 

  • Timoshenko SP and Goodier JN (1970). Theory of elasticity, 3rd edn. McGraw-Hill, New York

    Google Scholar 

Download references

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Correspondence to R. Kienzler.

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The contents of the present paper has been developed together with Prof. Dr. Dr. h. c. George Herrmann, Stanford University, California, who passed away on January 7, 2007.

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Kienzler, R. Reciprocity in fracture and defect mechanics. Int J Fract 147, 3–11 (2007). https://doi.org/10.1007/s10704-007-9115-0

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  • DOI: https://doi.org/10.1007/s10704-007-9115-0

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