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On smoothly growing bodies and the eshelby tensor

Abstract

A continuum mechanical theory of growing bodies is presented. It is assumed that the various parts of the body are identifiable. The growth of a body is manifested by mapping the identifiable elements of the growing body into a material manifold. Kinematics and stress theory are formulated on the basis of an infinite dimensional differentiable bundle structure for the configuration space. Stresses representing the forces associated with the growth of the body are analogous to the Eshelby tensor.

Sommario

Si propone una teoria meccanica dei corpi di massa crescente. Si postula che le varie parti del corpo siano identificabili. La crescita del corpo si manifesta mediante l'applicazione degli elementi identificabili del corpo in una varietà materiale. La cinematica e la teoria degli sforzi vengono formulati sulla base di un fibrato differenziabile a infinite dimensioni per lo spazio delle configurazioni. Gli sforzi associati alla crescita del corpo sono analoghi al tensore di Eshelby.

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References

  1. 1.

    DunfordN. and SchwartzJ.T., Linear Operators, Vol. 1, Wiley-Interscience, Chichester, 1971, pp. 43.

  2. 2.

    EshelbyJ.D., ‘Energy relations and the energy-momentum tensor in continuum mechanics’, In: M.F.Kanninen, W.F.Adler, A.R.Rosenfield, R.I.Jaffee (Editors) Inelastic Behavior of Solids, McGraw-Hill, New York, 1969, pp. 77–115.

  3. 3.

    Gurtin, M.E., ‘The nature of configurational forces’, Archive for Rational Mechanics and Analysis, 1995 (to appear).

  4. 4.

    MichorP.W., Manifolds of Differentiable Mappings, Shiva, London, 1980.

  5. 5.

    Segev, R., ‘On the definition of forces in continuum mechanics’, In: A. Blaquière, G. Leitmann (Editors), Dynamical Systems and Microphysics Control Theory and Mechanics, Academic Press, 1984, pp. 341–357.

  6. 6.

    SegevR., ‘Forces and the existence of stresses in invariant continuum mechanics’, Journal of Mathematical Physics, 27 (1986) 163–170.

  7. 7.

    SegevR. and deBottonG., ‘On the consistency conditions for force systems’, International Journal of Nonlinear Mechanics, 26 (1991) 47–59.

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Segev, R. On smoothly growing bodies and the eshelby tensor. Meccanica 31, 507–518 (1996). https://doi.org/10.1007/BF00420822

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Key words

  • Growing bodies
  • Kinematics
  • Velocity field
  • Eshelby tensor
  • Thermomechanics of continua