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A Note on Fracture Models Incorporating Surface Elasticity

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Abstract

Several recent papers that describe an approach to developing a theory of brittle fracture incorporating crack-surface elasticity have asserted that such models predict bounded stresses and strains at crack-tips in two dimensions. It is proved in this short note that the assertion is incorrect. While incorporating surface elasticity into fracture models in the setting of the linearized theory of elasticity does remove the square-root stress/strain singularity at crack-tips seen in classical theories that do not take account of crack-surface interfacial effects, it does not predict bounded stresses and strains but rather diminishes the singularity to being logarithmic.

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References

  1. Guritn, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)

    Google Scholar 

  2. Kim, C.I., Schiavone, P., Ru, C.-Q.: Analysis of a mode-III crack in the presence of surface elasticity and a prescribed non-uniform surface traction. Z. Angew. Math. Phys. 61, 555–564 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kim, C.I., Ru, C.-Q., Schiavone, P.: The effects of surface elasticity on an elastic solid with mode-III crack: complete solution. ASME J. Appl. Mech. 77(2), 021011 (2010)

    Article  ADS  Google Scholar 

  4. Antipov, Y.A., Schiavone, P.: Integro-differential equation for a finite crack in a strip with surface effects. Q. J. Mech. Appl. Math. 64(1), 87–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kim, C.I., Schiavone, P., Ru, C.-Q.: Analysis of plane-strain crack problems (mode-I & mode-II) in the presence of surface elasticity. J. Elast. 104, 397–420 (2011)

    Article  MathSciNet  Google Scholar 

  6. Kim, C.I., Schiavone, P., Ru, C.-Q.: Effect of surface elasticity on an interface crack in plane deformations. Proc. R. Soc. A (2011). doi:10.1098/rspa.2011.0311

    Google Scholar 

  7. Muskhelishvili, N.I.: Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics. P. Noordhoff, Groningen (1953)

    MATH  Google Scholar 

  8. Mikhlin, S.G., Prössdorf, S.: Singular Integral Operators. Springer, Berlin (1986)

    Book  Google Scholar 

  9. Sendova, T., Walton, J.R.: A new approach to the modeling and analysis of fracture through extension of continuum mechanics to the nanoscale. Math. Mech. Solids 15(3), 368–413 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sendova, T., Walton, J.R.: The effect of surface tension in modeling interfacial fracture. AIP Conf. Proc. 1301, 291–300 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  11. Rajagopal, K.R., Walton, J.R.: Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack. Int. J. Fract. 169(1), 39–48 (2011)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, USA

    Jay R. Walton

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  1. Jay R. Walton
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Correspondence to Jay R. Walton.

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Walton, J.R. A Note on Fracture Models Incorporating Surface Elasticity. J Elast 109, 95–102 (2012). https://doi.org/10.1007/s10659-011-9369-7

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  • DOI: https://doi.org/10.1007/s10659-011-9369-7

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