Civil Engineering Reference
In-Depth Information
Figure 3.9
Behaviour of ideal perfectly plastic materials.
Figure 3.9(d) contains the same information as Figs. 3.9(b) and (c) with the axes
superimposed and the origin for plastic strains placed at the end of the appropriate
vector of failure stress. For a perfectly plastic material the vector of plastic strain is
normal to the failure envelope, and this is known as the normality condition of perfect
plasticity.
Another common way of describing the flow rule for plastic straining is to define
a plastic potential envelope that is orthogonal to all the vectors of plastic straining,
as shown in Fig. 3.10. Then the material is perfectly plastic if the plastic potential is
the same as the failure envelope. This is called an associated flow rule as the plastic
potential is associated with the failure envelope. Of course the normality condition
and an associated flow rule are different ways of saying the same thing.
An important feature of plastic straining is that the strains depend on the state of
stress and do not depend on the small change of stress that causes the failure. This is
