﻿318 Mr. S. Lees on a Simple Model 



§ 4. Elastic Hysteresis Loop for Model. 



After slipping has occurred as just explained, the moment F 

 is caused to diminish, slipping will cease, and A l5 Bj, and Ci 

 (also A 2 , B 2 , and C 2 ) will move together. Thus if F l5 a\ be 

 the values of F and x at the instant that F is caused to 

 decrease, we shall have at first 



F I -F = (\ I + 2\,)(* 1 -*). . . . (13) 



Daring any change of the type given by (13), there will 

 be a constant amount of slip (reckoned from the neutral 

 state) given by 



0,t«y-T. ,.^g; . . (14) 



LK> 2 A 2 



It will be noticed that during the change given by (13), the 

 slope of the F, x curve is exactly the same as that given 

 by (9), i. e. as that for the neutral condition, also T 2 is now 

 at any instant given by 



T,-/*N == ^(w-ad, .... (15) 



since the slip does not alter, and dT 2 ld l v = \ 2 - 



As F goes on diminishing, ultimately becoming a force of 

 compression, a time will arrive when slipping will once more 

 occur. This will clearly be the case when 



T 2 = -/*N, (16). 



or from (15), when 



'--(¥-*) <"> 



This corresponds to a value of F given by 



F = \ lX - 2/aN = - 2/*N /- 1 + 1) + MV • (18) 



This result may be compared with (11). It will be noticed 

 that the value of F given by (18) is not in general the nega- 

 tive of that given bv (11). It is easy to see that further 

 compression beyond the value given by (16) will result in a 

 straight line law for F and x, such that 



g = X, ...... (19) 



For such further compressions, of course, sliding takes place. 

 If now the compression be gradually diminished, i. e. F be 



