Constrained elasticity

Paolo Podio-Guidugli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 4, page 341-350
  • ISSN: 1120-6330

Abstract

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Some foundational aspects of the constitutive theory of finite elasticity are considered in the case, regarded here as general, when internal kinematical constraints are imposed. The emphasis is on the algebraic-geometric structure induced by constraints. In particular, old and new examples of internal constraints are reviewed, and the material symmetry issue in the presence of constraints is discussed.

How to cite

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Podio-Guidugli, Paolo. "Constrained elasticity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.4 (1990): 341-350. <http://eudml.org/doc/244118>.

@article{Podio1990,
abstract = {Some foundational aspects of the constitutive theory of finite elasticity are considered in the case, regarded here as general, when internal kinematical constraints are imposed. The emphasis is on the algebraic-geometric structure induced by constraints. In particular, old and new examples of internal constraints are reviewed, and the material symmetry issue in the presence of constraints is discussed.},
author = {Podio-Guidugli, Paolo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Finite elasticity; Internal constraints; Material symmetries; internal kinematical constraints; material symmetry},
language = {eng},
month = {12},
number = {4},
pages = {341-350},
publisher = {Accademia Nazionale dei Lincei},
title = {Constrained elasticity},
url = {http://eudml.org/doc/244118},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Podio-Guidugli, Paolo
TI - Constrained elasticity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/12//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 4
SP - 341
EP - 350
AB - Some foundational aspects of the constitutive theory of finite elasticity are considered in the case, regarded here as general, when internal kinematical constraints are imposed. The emphasis is on the algebraic-geometric structure induced by constraints. In particular, old and new examples of internal constraints are reviewed, and the material symmetry issue in the presence of constraints is discussed.
LA - eng
KW - Finite elasticity; Internal constraints; Material symmetries; internal kinematical constraints; material symmetry
UR - http://eudml.org/doc/244118
ER -

References

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  1. PODIO-GUIDUGLI, P. - VIANELLO, M., Constraint manifolds for isotropic solids. Arch. Rational Mech. Anal., 105, 1989, 105-121. Zbl0678.73004MR968457DOI10.1007/BF00250833
  2. GURTIN, M. E. - PODIO-GUIDUGLI, P., The thermodynamics of constrained materials. Arch. Rational Mech. Anal., 51, 1973, 192-208. Zbl0263.73004MR356720
  3. COHEN, H. - WANG, C.-C., On the response and symmetry of elastic materials with internal constraints. Arch. Rational Mech. Anal., 99, 1987, 1-36. Zbl0629.73003MR881283DOI10.1007/BF00251389
  4. GURTIN, M. E., An Introduction to Continuum Mechanics. Academic Press, 1981. Zbl0559.73001MR636255
  5. NOLL, W., Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal., 52, 1973, 62-92. Reprinted in: NOLL, W., The Foundations of Mechanics and Thermodynamics. Springer Verlag, 1974. Zbl0284.73002MR351238
  6. TRUESDELL, C. - NOLL, W., The Non-Linear Field Theories of Mechanics. In: S. FLÜGGE (ed.), Handbüch der Physik. Springer Verlag, vol. III/3, 1965. Zbl0779.73004MR193816
  7. CAPRIZ, G. - PODIO-GUIDUGLI, P., Materials with spherical structure. Arch. Rational Mech. Anal., 75, 1981, 269-279. Zbl0484.73002MR605892DOI10.1007/BF00250786
  8. PODIO-GUIDUGLI, P., An exact derivation of the thin plate equation. J. of Elasticity, 22, 1989, 121-133. Zbl0692.73049MR1040755DOI10.1007/BF00041107
  9. ERICKSEN, J. L., Constitutive theory for some constrained elastic crystals. Int. J. Solids Structures, 22, 1986, 951-964. Zbl0595.73001
  10. PODIO-GUIDUGLI, P., The Piola-Kirchhoff stress may depend linearly on the deformation gradient. J. of Elasticity, 17, 1987, 183-187. Zbl0603.73035MR885603DOI10.1007/BF00043023
  11. BELL, J. F., Continuum plasticity at finite strain for stress paths of arbitrary composition and direction. Arch. Rational Mech. Anal., 84, 1983, 139-170. Zbl0523.73029MR713122DOI10.1007/BF00252130
  12. NOLL, W., A mathematical theory of the mechanical behavior of continuos media. Arch. Rational Mech. Anal., 2, 1958, 197-226. Reprinted in: NOLL, W., The Foundations of Mechanics and Thermodynamics. Springer Verlag, 1974. Zbl0083.39303MR105862
  13. GURTIN, M. E. - WILLIAMS, W. O., On the inclusion of the complete symmetry group in the unimodular group. Arch. Rational Mech. Anal., 23, 1966, 163-172. Zbl0168.45801MR231568

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