Effective plastic strain rate:

( ) ( ) ( ) ( ) ( ) ( )[ ]{ } 2/12222222

3

2

3

2 pyz

pxz

pxy

pzz

pyy

pxx

pij

pij

p εεεεεεεεε &&&&&&&&& +++++==

Effective plastic strain:

∫= dtpp εε &

For example uniaxial tension in the x-direction the strain rates are

0

0

0

5.0

5.0

=

=

=

−=

−=

=

pyz

pxz

pxy

pzz

pyy

pxx

εε

εεε

εεεε

&

&

&

&&

&&

&&

Where the -0.5 factors are from conservation of volume (“Plastic Poisson’s Ratio” = 0.5). The effective plastic strain rate is

( ) ( ) ( ){ } ( ) εεεεεε &&&&&& ==−+−+= 22/1222

2

3

3

25.05.0

3

2p

So that for uniaxial loading the effective plastic strain rate is equal to the strain rate in the

loading direction (this is the point of the 3/2 factor). This is similar conceptually to effective stress.