Si dimostra che ci sono valide ragioni per considerare la teoria standard dei vincoli interni, nella meccanica dei continui, insufficientemente generale. In particolare, con l’unica eccezione dell’iperelasticità, l’extra-stress dovrebbe dipendere anche dai moltiplicatori di Lagrange, cioè, dallo stress che non effettua lavoro (virtuale).
@article{RLINA_1981_8_70_6_256_0, author = {Stuart S. Antman}, title = {Material constraints in continuum mechanics}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {70}, year = {1981}, pages = {256-264}, zbl = {0508.73002}, language = {en}, url = {http://dml.mathdoc.fr/item/RLINA_1981_8_70_6_256_0} }
Antman, Stuart S. Material constraints in continuum mechanics. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 70 (1981) pp. 256-264. http://gdmltest.u-ga.fr/item/RLINA_1981_8_70_6_256_0/
[1] General solutions for plane extensible elasticae having nonlinear stress-strain laws, «Quart. Appl. Math.», 29, 35-47. | Zbl 0157.56505
(1968) -[2] Global behavior of buckled states of nonlinearly elastic rods, «SIAM Rev.», 20, 513-566. (1980) - Corrections and additions, Ibid. 22, 186-187. | Zbl 0395.73039
and (1978) -[3] A theory of the effects of pressure on finite elastic shear, in «Rheology», Vol. 1, edited by , , and , Plenum, 305-311.
and (1980) -[4] Existence of caloric equations of state in thermodynamics, «J. Chem. Phys.», 40, 1116-1125.
and (1964) -[5] The motion of slightly compressible fluids viewed as a motion with strong constraining forces, «Ann. Math.», 105, 141-200. | Zbl 0373.76007
(1977) -[6] Large elastic deformations of homogeneous anisotropic materials, «J. Rational Mech. Anal.», 3, 281-301. | Zbl 0055.18103
and (1954) -[7] Thermodynamics of a continuum with internal constraints, «Int. J. Engg. Sci.», 8, 891-908. | Zbl 0218.73006
, and (1970) -[8] Finite deformation of an almost incompressible solid, «I.U.T.A.M. International Symposium on Second Order Effects in Elasticity, Plasticity, and Fuid Dynamics», Haifa, Israel, 1962, edited by and , MacMillan, New York, 200-216.
(1964) -[9]
and (1965) - The Non-linear Field Theories of Mechanics, «Handbuch der Physik III/3», Springer-Verlag.[10] Pressure dependence and dilatancy of plastic flow, in “Theoretical and Applied Mechanics, Proc. XV Int. Cong.” edited by and , North Holland, 377-386. | MR 617023
and (1980) -