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A Model of the Evolution of a Two-dimensional Defective Structure

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Abstract

A model of the anelastic evolution law of a two-dimensional defective solid crystal body is proposed. Assuming that the material body is made of triclinic crystals and that the evolution process does not alter the basic material symmetry group, we postulate that the evolution is driven by the present state of the density of the distribution of defects. We show that a linear relation between the inhomogeneity velocity gradient and the torsion tensor is rich enough to model such phenomena as relaxation of defects and dislocation pile-up.

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References

  1. C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Springer, New York (2000).

    Google Scholar 

  2. G.F.D. Duff, Partial Differential Equations. University of Toronto Press, Toronto (1956).

    Google Scholar 

  3. M. Elżanowski and M. Epstein, On the intrinsic evolution of material inhomogeneities. In: Proc. the 2nd Canadian Conf. on Nolinear Solid Mechanics, Vancouver, Canada (2002) in press.

  4. M. Elżanowski, M. Epstein and J. Śniatycki, G-structures and material homogeneity. J. Elasticity 23(2/3) (1990) 167–180.

    Google Scholar 

  5. M. Epstein, A Question of constant strain. J. Elasticity 17 (1987) 23–34.

    Google Scholar 

  6. M. Epstein and G.A. Maugin, On the geometrical material structure of anelasticity. Acta Mech. 115 (1996) 119–134.

    Google Scholar 

  7. M. Epstein and G.A. Maugin, Thermomechanics of volumetric growth in uniform bodies. Internat. J. Plasticity 16 (2000) 951–978.

    Google Scholar 

  8. M.E. Gurtin, A Gradient theory of single crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 5–32.

    Google Scholar 

  9. P.M. Naghdi and A.R. Srinivasa, A dynamical theory of structured solids. I Basic developments. II Special constitutive equations and special cases of the theory. Phil. Trans. Roy. Soc. London A 345 (1993) 425–476.

    Google Scholar 

  10. W. Noll, Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27 (1967) 1–32.

    Google Scholar 

  11. C. Truesdell and W. Noll, The Non-Linear Field Throeries of Mechanics. Handbuch der Physik, Vol. III/3. Springer, Berlin (1965).

    Google Scholar 

  12. C.-C. Wang, On the geometric structure of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations. Arch. Rational Mech. Anal. 27 (1967) 33–94.

    Google Scholar 

  13. C.-C. Wang and C. Truesdell, Introduction to Rational Elasticity. Nordhoff, Leyden (1973).

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, The University of Calgary, Calgary, AB, Canada

    Marcelo Epstein

  2. Department of Mathematical Sciences, Portland State University, Portland, OR, U.S.A.

    Marek Elżanowski

Authors
  1. Marcelo Epstein
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  2. Marek Elżanowski
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Epstein, M., Elżanowski, M. A Model of the Evolution of a Two-dimensional Defective Structure. Journal of Elasticity 70, 255–265 (2003). https://doi.org/10.1023/B:ELAS.0000005550.04350.7c

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  • DOI: https://doi.org/10.1023/B:ELAS.0000005550.04350.7c

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