By R. W. Dickey

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Extra resources for Nonlinear Elasticity. Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 16–18, 1973

Sample text

I . e . the spatial gradient of the temperature field, at £ and t, is the vector fl(£,t)S *5e(x,t)|ssX(£)t). The histories up to t of the deformation gradient and tem­ perature at £ are functions F* and 6*, on [ 0 , oo)^ d e ­ fined by E^s) =F(&, t - s ) , e^s) =0(£, t - s ) , s € [ 0 , oo). A material is characterized by constitutive assumptions which restrict the c l a s s of p r o c e s s e s . 3) I a = q, T, i\9 g, 2> a n d E a r e present v a l u e s , i . e . values at time t at the point under consideration.

To render the energy See, for example, Coleman and Noll [ 2 2 ] , §15. Note, in particular, their Thm. 14 on page 124. The idea that the en­ ergy criterion has a thermodynamical basis was discussed at length by Gibbs [ 23] and Duhem [ 21]. 46 CRITERION FOR STABILITY criterion precise and to give it a dynamical significance, let us suppose that a semi-metric d has been defined on the domain \$1 of r e ° 5 then d(f , £) = 0 < d(f 2 , f 1 ) = d(£ ! , f2) < cKf1, f) + d(f, f 2 ) , for all configurations J , J , and ^f in \$1 .

Bauer, L. , K e l l e r , H . B. and R e i s s , E. L. , Axially Symmetric Buckling of Rigidly Clamped S p h e r i c a l S h e l l s , I n t e r n a t i o n a l J. of N o n - L i n e a r M e c h . 8. (1973), p p . 3 1 - 3 9 . 4. S r u b s h c h i k , L. S. and I u d o v i c h , V. I. , The A s y m p ­ t o t i c I n t e g r a t i o n of t h e System of E q u a t i o n s for t h e Large D e f l e c t i o n of S y m m e t r i c a l l y Loaded S h e l l s of R e v o l u t i o n , P r i k l . M a t .