K 



THE THERMODYNAMICS OF STRAINED 

 ELASTIC SOLIDS 



The Conditions of Internal and External Equilib- 

 rium FOR Solids in Contact with Fluids with Regard 

 to all Possible States of Strain of the Solids 



[Gibbs, I, pp. m-218] 



JAMES RICE 



Note. In order to follow this part of Gibbs' work the reader must know 

 Bomething about the mathematical treatment of the relations which 

 exist between the stresses set up in an elastic medium bj the action of 

 external forces on it, and the strains which accompany these stresses. 

 In the study of the thermodynamics of these media, such relations 

 take the place of the equation of state in the thermodynamics of a fluid 

 medium. The treatment of Gibbs is formally somewhat more compli- 

 cated than that usually employed, by reason of his desire at the outset 

 to make use of two sets of axes of reference which need not be regarded 

 as identical, although they are similar, i.e., capable of superposition 

 (p. 185). It will therefore be advisable to deal with these matters in 

 a less complicated manner at first. In consequence we shall have to 

 prefix to the commentary proper a rather long exposition of the analy- 

 sis of strain and stress, with some account of the thermodynamics of a 

 single strained body. 



I. Exposition of Elastic Solid Theory So Far As Needed 



for Following Gibbs' Treatment of the 



Contact of Fluids and Solids 



1. Analysis of Strain. When a body is deformed or strained, 

 its parts undergo a change of relative position. In order to 

 deal with this in the classical mathematical way, we conceive 

 the body to be constituted of particles each of which has in 

 any assigned state of strain definite coordinates with regard to 

 assigned axes of reference; and yet we compromise with these 



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