BOOK REVIEWS

I . I. B u g a k o v , CREEP

OFPOLYMER

MATERIALS*

Reviewedby G. N . S a v i n

and Ya.

Ya.

Ryshehitskii

The monograph gives the general theoretical principles and methods for solving problems in the theory of viscoelasticity (the theory of creep) with application to high molecular materials. The content of the book r e p r e s e n t s an expansion of the course of lectures on the mechanics of polymers which the author reads at Leningrad State University, in the Department of Mathematics and Mechanics. The book consists of an introduction and three parts, comprising ten chapters. The introduction gives general information on polymer materials, and a historical review of the theory of viscoelasticity. The first part . G e n e r a l Theory" consists of two chapters. The first chapter "Creep with Elongation, Compression, and Shear" discusses the creep of polymer samples with elongation, compression, and shear; the principles of the combination of s t r e s s e s and the combination of deformations are discussed separately; the applicability of the principle of combination in the description of the creep of polymer materials, particularly amorphous, is demonstrated; here, the discussions are illustrated by the data of experiments on celluloid. Creep equations are constructed and some of the overall properties of these equations are evaluated; the Kohlrausch effect is described. The second chapter . C r e e p with a Complex Stressed State, is devoted to the determining equations of the theory of viscoelasticity. The tensors of the s t r e s s and the deformation are introduced; first, anisetropic materials are discussed and then, isotropic materials are considered in more detail; the results of experiments on creep for Plexiglas are given. Nonlinear creep equations, analogous to those proposed by M. I. Rozovskii and N. Kh. Arutyunyan, are evaluated. The second part . L i n e a r Theory" consists of three chapters. The third chapter "The Equations of Creep" discusses linear creep equations. It discusses the cases of elongation and compression; functions of a material of the k-th order are derived; the chapter gives the forms for writing the creep equations, the elements of the algebra of linear operators, the connection between the functions of the material, and inequalities for these functions. This is followed by a discussion of the creep equations in tensor form for anisotropie materials; equations are written for partial cases of anisotropy of the mechanical properties. The equations of creep in the isotropic case are discussed separately. The fourth chapter ,Methods for Calculating Deformation P r o c e s s e s " continues the discussion of the linear creep operator and its properties. It gives the value of the operator as a stepwise function of the time; a study is made of the construction of theoretical creep curves with a piecewise-linear change in the loads. For an approximate solution of creep equations with an a r b i t r a r y right-hand part, the method of finite differences is proposed; the chapter briefly describes the method of the L a p l a c e - C a r s o n transform, and a fractional-exponential kernal of the creep; several concepts from algebra, used in the interpretation of operator expressions are given for fractional-exponential operator expressions. *Nauka, Moscow (1973), 288 pp, Translated from Prikladnaya Mekhanika, Vol. 10, No. 1, pp. 104-1!0, January, 1974. 9 19 75 Plenum Publishhzg Corporation, 22 7 West 1 7th Street, New York, N. Y. 10011. No part o f this publieation may be reproduced, stored in a retrieval system, or transmitted, in any fi~rm or by an), means, eh,ctrotzie, mechanical, photoeopybzg, microfib77ing, recording or otherwise, without written permission ~[ the publisher. A copy o f this article is available frcmz the publisher for $15.00.

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The fifth c h a p t e r " N 0 n i s o t h e r m a l C r e e p " d i s c u s s e s f i r s t the c a s e of pure s h e a r ; the p r i n c i p l e of t e m p e r a t u r e - t i m e c o r r e s p o n d e n c e is used and t h e r m o r h e o l o g i c a l l y s i m p l e m a t e r i a l s a r e d i s c u s s e d ; the e q u a tions of t h e r m o c r e e p a r e given and t h e i r p r o p e r t i e s a r e analyzed. The c h a p t e r brings out the t h e r m o d y n a m i c a s p e c t of the t i m e s c a l e ; n o n - i s o t h e r m a l f r a c t i o n a l - e x p o n e n t i a l o p e r a t o r s a r e h-~troduced. The c h a p t e r a l s o d i s c u s s e s t h e r m a l expansion and a c o m p l e x s t r e s s e d s t a t e . What has been s e t forth in the f i r s t two s e c t i o n s of the c h a p t e r is g e n e r a l i z e d f o r the c a s e of nonlinear c r e e p . The third p a r t ,Methods for Solving P r o b l e m s of C r e e p , contains five c h a p t e r s . In the sixth c h a p t e r " O v e r a l l P r o p e r t i e s of the Solution of P r o b l e m s of C r e e p , a study is made of the o v e r a l l p r o p e r t i e s of b o u n d a r y - v a l u e p r o b l e m s in the l i n e a r and nonlinear t h e o r y of c r e e p . T h i s r e l a t e s , above all, to the conditions f o r the i n v a r i a n c y and the additivity of the solution in t i m e . The linear, theory admits of a g r e a t e r n u m b e r of p r o p e r t i e s , which a r e also d i s c u s s e d . The seventh c h a p t e r " V i s c o e l a s t i c A n a l o g i e s , contains i n f o r m a t i o n on v i s c o e l a s t i c analogies and t h e i r application. T h e r e is a r a t h e r c o m p l e t e exposition of the A l f r e ' analogy, and a detailed study is made, using this analogy, of the p r o b l e m of the bending of a b e a m . The c h a p t e r gives m o r e g e n e r a l methods of solution: the V o l t e r r a principle, the principle of c o r r e s p o n d e n c e (the method of t h e L a p l a c e - - C a r s o n t r a n s form), the method of a p p r o x i m a t i o n , the Sheper a p p r o x i m a t e method. By way of illustration, the c h a p t e r gives the solution to a n u m b e r of uncomplicated p r o b l e m s : the plane a x i s y m m e t r i c d e f o r m a t i o n of o r t h o tropic and i s o t r o p i c thick-walled tubes; the p r e s s u r e of a s p h e r e in a h a l f - s p a c e ; the l o n g i t u d i n a l - t r a n s v e r s e bending of a b e a m . The eighth e h a p t e r n C o m p o s i t e Bodies" g e n e r a l i z e s the p r e v i o u s l y d i s c u s s e d p r o b l e m of the d e f o r m a tion of a tube to the c a s e of a c o m p o s i t e tube (tubes with a r e i n f o r c e d shell). E x a m p l e s of actual c a l c u l a tions and c u r v e s a r e given. The r~inth chapter, " P r o b l e m s in the Nonlinear T h e o r y of C r e e p , , contains solutions of a n u m b e r of p r o b l e m s of c r e e p f o r m a t e r i a l s , whose t h e o l o g i c a l equations have the f o r m of the nonlinear c r e e p e q u a tions introduced in the second c h a p t e r . The a r t i c l e d i s c u s s e s the p r o b l e m of the elongation of a rod lattice, and brings out the effect of equalization of the s t r e s s e s in the r o d s . It d e s c r i b e s nonlinear p r o b l e m s of p u r e bending, of the e q u i l i b r i u m of a t h i c k - w a l l e d tube (solved in the l i n e a r s t a t e m e n t in the seventh c h a p ter), and of a round c y l i n d e r rotating around its longitudinal a x i s . The tenth c h a p t e r " T e m p e r a t u r e S t r e s s e s , d i s c u s s e s the c r e e p of p o l y m e r s under the effect of t e m p e r a t u r e , and g i v e s a c o m p l e t e s y s t e m of equations for t h e r m o c r e e p ; the solution and its p r o p e r t i e s a r e investigated~ and the c a s e s of homogeneous and s t e a d y - s t a t e t e m p e r a t u r e fields a r e t r e a t e d s e p a r a t e l y . A study is m a d e of the p r o b l e m of the r e s i d u a l s t r e s s e s and d e f o r m a t i o n s in a cooled body. As an example, the p r o b l e m of an inhomogeneous cooled s p h e r e is solved in the l i n e a r s t a t e m e n t . At the end of the book t h e r e is a b i b l i o g r a p h y with 237 e n t r i e s . The m o n o g r a p h is written c l e a r l y and understandably. The definite c o m p a c t n e s s of the exposition, in p l a c e s the s k e t c h i n e s s , is obviously due to the d e s i r e of the author to elucidate the questions as c o m p l e t e l y as p o s s i b l e within the f r a m e w o r k of a s p e c i a l u n i v e r s i t y c o u r s e . A m o r e complete exposition of g e n e r a l i n f o r m a t i o n f r e m the physics and c h e m i s t r y of p o l y m e r s would be v e r y much in place. The book is of undoubted scientific and methodological value. It should evoke s p e c i a l i n t e r e s t on the p a r t of s p e c i a l i s t s who a r e involved in e x p e r i m e n t a l investigations in the field of the m e c h a n i c s of p o l y mers.

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