Page 152 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of a composite layer 137

Assuming that Up = U,,(o),where o is the stress intensity specified by Eqs. (4.19)
or (4.24), we get

The explicit form of these equations for the plane stress state is:

where

dUp dj
do(o) = -- . . (4.45)
a do
To determine parameter I-, assume that plastic potential Upbeing on the one hand a
function of o,can be treated as the work performed by stresses on plastic strains, Le.,

Substituting strain increments from Eqs. (4.44) and taking into account Eq. (4.24)
for o we get

With due regard to Eq. (4.45) we arrive at the simple and natural relationship
di. = do/o. Thus, Eq. (4.45) acquires the form

dodU,,
do(a) = -- (4.46)
o2 da
and Eqs. (4.42H4.44) result in the following constitutive equations of the flow
theory:

(4.47)