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Laws of Evolution of Cracks in Plates in Terms of Stress Resultants

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Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 104))

Abstract

The laws of evolution of a crack that starts at the edge of a plate and progresses toward its interior are derived in terms of stress and moment resultants written in the reference configuration of the plate. A modified form of the J-integral in terms of stress and moment resultants is also derived.

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References

  • Capriz, G. (1985) Continua with latent microstructure, Arch. Rational Mech. Anal. 90, 43–56.

    Article  MathSciNet  MATH  Google Scholar 

  • Capriz, G. (1989) Continua with Micro structure, Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Ericksen, J. L. and Truesdell, C. A. (1958) Exact theory of stress and strain in rods and shells, Arch. Rational Mech. Anal. 1, 295–323.

    Article  MathSciNet  MATH  Google Scholar 

  • Gurtin, M. E. (1995) The nature of configurational forces, Arch. Rational Mech. Anal. 131, 67–100.

    Article  MathSciNet  MATH  Google Scholar 

  • Gurtin, M. E. (2000) Configurational Forces as Basic Concepts in Continuum Physics, Springer-Verlag, Berlin.

    Google Scholar 

  • Gurtin, M. E. and Podio-Guidugli, P. (1996) Configurational forces and the basic laws for crack propagation, J. Mech. Phys. Solids 44, 133–154.

    Article  MathSciNet  Google Scholar 

  • Mariano, P. M. (2000) Configurational forces in continua with microstructure, Z. angew. Math. Phys. ZAMP 51, 752–791.

    Article  MathSciNet  MATH  Google Scholar 

  • Mariano, P. M. (2001) Multifield theories in mechanics of solids, Adv. Appl. Mech., 38, 1–93.

    Article  MathSciNet  Google Scholar 

  • Mariano, P. M., Augusti, G. and Stazi, F. L. (2002) Cracks in plates: the driving force in terms of stress and moment resultants, in preparation.

    Google Scholar 

  • Maugin, G. A. (1992) The Thermomechanics of Plasticity and Fracture, Cambridge University Press, Cambridge.

    Book  MATH  Google Scholar 

  • Maugin, G. A. (1994) On the J-integral and energy-release rates in dynamical fracture. Acta Mech. 105, 33–47.

    Article  MathSciNet  MATH  Google Scholar 

  • Naghdi, P. M. (1972) The theory of shells. In Handbuk der Physics, VIa/2 (C. Truesdell ed.), 425–640, Springer-Verlag, Berlin.

    Google Scholar 

  • Simo, J. C. and Fox, D. D. (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization, Comp. Meth. Appl. Mech. Engng 72, 267–304.

    Article  MathSciNet  MATH  Google Scholar 

  • Simo, J. C., Marsden, J. E. and Krishnaprasad, P. S. (1988) The Hamiltonian structure of nonlinear elasticity: The material and convective representation of solids, rods and plates, Arch. Rational Mech. Anal. 104, 125–183.

    Article  MathSciNet  MATH  Google Scholar 

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© 2002 Springer Science+Business Media Dordrecht

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Augusti, G., Mariano, P.M., Stazi, F.L. (2002). Laws of Evolution of Cracks in Plates in Terms of Stress Resultants. In: Drew, H.R., Pellegrino, S. (eds) New Approaches to Structural Mechanics, Shells and Biological Structures. Solid Mechanics and Its Applications, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9930-6_4

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  • DOI: https://doi.org/10.1007/978-94-015-9930-6_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6120-1

  • Online ISBN: 978-94-015-9930-6

  • eBook Packages: Springer Book Archive

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