Constrained elasticity
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 341-350.

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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.
Si espongono alcuni aspetti di fondamento della teoria costitutiva dell'elasticità finita nel caso in cui si impongano vincoli cinematici interni, caso che è qui riguardato come generale. L'attenzione è concentrata sulla struttura algebrico-geometrica indotta dai vincoli. In particolare, si passano in rassegna vecchi e nuovi esempi di vincoli interni e si discute la questione delle simmetrie materiali in presenza di vincoli.
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Podio-Guidugli, Paolo. Constrained elasticity. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 341-350. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_4_a9/

[1] P. Podio-Guidugli - M. Vianello, Constraint manifolds for isotropic solids. Arch. Rational Mech. Anal., 105, 1989, 105-121. | DOI | MR | Zbl

[2] M. E. Gurtin - P. Podio-Guidugli, The thermodynamics of constrained materials. Arch. Rational Mech. Anal., 51, 1973, 192-208. | MR | Zbl

[3] H. Cohen - C.-C. Wang, On the response and symmetry of elastic materials with internal constraints. Arch. Rational Mech. Anal., 99, 1987, 1-36. | DOI | MR | Zbl

[4] M. E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, 1981. | MR | Zbl

[5] W. Noll, Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal., 52, 1973, 62-92. Reprinted in: W. Noll, The Foundations of Mechanics and Thermodynamics. Springer Verlag, 1974. | MR | Zbl

[6] C. Truesdell - W. Noll, The Non-Linear Field Theories of Mechanics. In: S. FLÜGGE (ed.), Handbüch der Physik. Springer Verlag, vol. III/3, 1965. | MR | Zbl

[7] G. Capriz - P. Podio-Guidugli, Materials with spherical structure. Arch. Rational Mech. Anal., 75, 1981, 269-279. | DOI | MR | Zbl

[8] P. Podio-Guidugli, An exact derivation of the thin plate equation. J. of Elasticity, 22, 1989, 121-133. | DOI | MR | Zbl

[9] J. L. Ericksen, Constitutive theory for some constrained elastic crystals. Int. J. Solids Structures, 22, 1986, 951-964. | Zbl

[10] P. Podio-Guidugli, The Piola-Kirchhoff stress may depend linearly on the deformation gradient. J. of Elasticity, 17, 1987, 183-187. | DOI | MR | Zbl

[11] J. F. Bell, Continuum plasticity at finite strain for stress paths of arbitrary composition and direction. Arch. Rational Mech. Anal., 84, 1983, 139-170. | DOI | MR | Zbl

[12] W. Noll, A mathematical theory of the mechanical behavior of continuos media. Arch. Rational Mech. Anal., 2, 1958, 197-226. Reprinted in: W. Noll, The Foundations of Mechanics and Thermodynamics. Springer Verlag, 1974. | MR | Zbl

[13] M. E. Gurtin - W. O. Williams, On the inclusion of the complete symmetry group in the unimodular group. Arch. Rational Mech. Anal., 23, 1966, 163-172. | MR | Zbl