TABLE OF CONTENTS Plastic behaviour characterized by irreversibility of stress paths and the development of permanent strain changes after a stress cycle can be described in a variety of ways. One form of such description has been given in Sec. 4.3. Another general method is presented here.
This approach assumes a priori the existence of a rate process which may be written directly as
| (4.144) |  |
in which the matrix D * depends not only on the stress ? and the state of parameters ?, but also on the direction of the applied stress (or strain) rate 
(or 
).58 A slightly less ambitious description arises if we accept the dependence of D * only on two directions - those of loading and unloading. If in the general stress space we specify a 'loading' direction by a unit vector n given at every point (and also depending on the state parameters ?), as shown in Fig. 4.9, we can describe plastic loading and unloading by the sign of the projection 
. Thus
| (4.145) |  |
while 
is a neutral direction in which only elastic straining occurs. One can now write quite generally that
| (4.146) |  |
where the matrices 
and 
depend only on the state described by ? and ?.
The specification of 
and 
must be such that in the neutral direction of the stress increment
