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Nonlinear Dynamics of Elastic Bodies by Z. Wesolowski

By Z. Wesolowski

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Jtat. 1. appl. (5), 4, 33, 1943. , On the thermodynamic potential for continuums with reversible deformations. Some possible types. Kecca- nica3 l , 15, 1966. 8. Boillat, G. l. • ' Su alcune classi di potenziali termodinamici come conseguenza dell'esistenza di particolari onde di discontinuita nella meccanica dei continui con deformazioni finite, Rend. Sem. Mat. 9. Padova 3 5l,l,l974. , Thermo-mechanics of rubber-like materials. Phil. Trans. Roy. Soc. Lond. 3 276, 371, 197lJ. 39 Topics in Elastodynamics CHAPTER IV SIGNORINI'S PROBLEM LINEARIZATION.

Manacorda R E F E R E NC E S 1. , Trasformazioni termoelastiche finite, Mern. II, Ann. Nat. pur>a appZ. 2. (4), 30, 1, 1949. ::ompatibilita" tra la elastostatica classica e la teoria delle ni e1astiche finite, Ace. Naz. Nat. 3. Lincei~ de~orrnazi£ Rend. CZ. Fis. Mat. (8), 8, 276; 1950. , Orientamenti principali di un corpo elastica rispetto al1a sua sollecitazione totale, Mem. Ace. It. (7), 13, 1139, 1943. 4. , Memoria sobre a torno das pontes d'applica~~o, rota;~o das em for~as Nem. Ac. R. Sci.

5) If we chose =J ~ - ( 3. 6) 1 we obtain the particular but noticeable case, when T - =- P -1 + P 0 IaE~ IT ( 3. 7) For a Signorini's thermoelastic incompressible solid (Sign£ rini 9 ) J - f(fl,T) =0 , ( 3. 4) we obtain n = ll ae ( 3. ,t-s),O~s<+oo I;-the history of deformation to the time t. In such a theory, it seems reasonable to introduce constraints expressed by means of functional relations of the form r(X,Ft (s) ) = 0. However, under the hypotheses usually accept;d in the theory of simple bodies, it can be nrove~ that r must reduce to an ordinary function of the i~stantuneous deternination of F.

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