On the thermodynamic potential for continuums with reversible transformations- some possible types. (English) Zbl 0163.46304
Keywords:
mechanics of solidsReferences:
| [1] | To the first criterion conforms the elasticity of second grade ofA. Signorini, Trasformazioni termoelastiche finite, Memoria II, Annali di Matematica pura e applicata, Serie IV, 30, 1–72, 1949. To the second, that ofC. Tolotti,Deformazioni elastiche: onde ordinarie di discontinuità e casi di solidi elastici isotropi, Rend. Mat. Appl., Serie V, 4, 34–59, 1943. See alsoA. Bressan,Sulla propagazione delle onde ordinarie di discontinuità nei sistemi a trasformazioni reversibili, Rend. Sem. Mat. University of Padova. V. 33, 99–139, 1963. · Zbl 0036.39502 · doi:10.1007/BF02414999 |
| [2] | Signorini A., Loc. cit.: note note (1), p. 34. |
| [3] | Expression (37) is an immediate consequence of what is said in loc. cit. in note (2). See alsoG. Grioli,Mathematical Theory of Elastic Equilibrium (Recent Results), Ergebnisse der Angewandten Mathematik, 7. Springer-Verlag 1962, p. 24. |
| [4] | With reference to the impossibility that the Eulerian stress is linear in {\(\epsilon\)} r8 (i) ,P. G. Bordoni has demonstrated the possibility that theX rs are expressed by the product of linear functions of the {\(\epsilon\)} r8 (i) by a same function of the invariantsI 1 (i) ,D (i):Sopra le trasformazioni termostatiche finite di certi solidi omogenei ed isotropi, Rend Mat. pura e appl. V. XIII, S.V., 237–266, 1953. |
| [5] | In the case of incompressible bodies (38) reduces to the expression proposed byD. C. Treloar,The elasticity of a network of long chain molecules, Trans Faraday SOC. 39, 1943, pp. 36–41 and 241–246. · doi:10.1039/tf9433900036 |
| [6] | If we compel in (50) the constantv to reduce to zero the coefficient of \(I_1 ^{(\rho )_2 }\) we get the expression for the incompressible bodies as proposed byM. Mooney,A Theory of Large Elastic Deformations, J. Appl. Phys. XI, 1940, pp. 582–592. · JFM 66.1021.04 · doi:10.1063/1.1712836 |
| [7] | Signorini, Loc. Cit. in note (1), p. 37. |
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