Thermodynamics of monopolar continuum of grade $n$

Bucháček, Karel

doi:10.21136/AM.1971.103368

Geodesic

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Thermodynamics of monopolar continuum of grade

n

Bucháček, Karel

Applications of Mathematics, Tome 16 (1971) no. 5, pp. 370-383.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Résumé

Contrary to the theory of the simple material it is assumed that the values of physical quantities at a point are arrected by the deformation history of a finite neighborhood of the point. In the case of the monopolar continuum of grade

n

, the physical quantities are in a functional dependence on the temperature and, moreover, on 4n

d e f o r m a t i o n g r a d i e n t s w h i c h a r e f o u n d f r o m a s i n g l e s h i f t f u n c t i o n . E q u a t i o n s o f e q u i l i b r i u m a n d t h e b o u n d a r y v a l u e s f o r a l l

s t r e s s t e n s o r s a r e e v a l u a t e d o n t h e b a s i s o f t h e F i r s t L a w o f T h e r m o d y n a m i c s . I n t r o d u c i n g t h e H i l b e r t s p a c e w i t h t h e n o r m w h i c h e x p r e s s e s t h e f a d i n g o f t h e m e m o r y i t i s p o s s i b l e t o d e r i v e t h e s y s t e m o f c o n s t i t u t i v e e q u a t i o n s f r o m t h e S e c o n d L a w o f T h e r m o d y n a m i c s . T h e s e e q u a t i o n s e n a b l e u s t o e v a l u a t e t h e e n t r o p y a s w e l l a s a l l s t r e s s t e n s o r s p r o v i d e d t h e f u n c t i o n a l d e p e n d e n c e o f t h e f r e e e n e r g y o n t h e h i s t o r y o f

n$ deformation gradients and on the history of temperature is given.

MR Zbl

DOI : 10.21136/AM.1971.103368

Classification : 74A15

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Bucháček, Karel. Thermodynamics of monopolar continuum of grade $n$. Applications of Mathematics, Tome 16 (1971) no. 5, pp. 370-383. doi : 10.21136/AM.1971.103368. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1971.103368/

Cité par

Šilhavý, Miroslav Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity, Applications of Mathematics, Volume 37 (1992) no. 5, pp. 383-400 | DOI:10.21136/am.1992.104518 | Zbl:0770.73031
Cheverton, K. J.; Beatty, M. F. On the mathematical theory of the mechanical behavior of some non-simple materials, Archive for Rational Mechanics and Analysis, Volume 60 (1975), pp. 1-16 | DOI:10.1007/bf00281466 | Zbl:0344.73010

Cité par 2 documents. Sources : zbMATH