Constant volume (incompressibility) condition

It has been mentioned that plastic deformation occurs at constant volume so that these strain increments are related in the following manner. With no change in volume, the differential of the volume of the gauge region will be zero, i.e.

d(lwt) = d(lowoto) = 0

and we obtain

(dl . wt) + (dw . lt) + (dt . lw) = 0

or, dividing by lwt,

(dl/l )+(dw/w) +(dt/t) = 0

i.e.

dε1 + dε2 + dε3 = 0

Thus for constant volume deformation, the sum of the principal strain increments is zero.