Nonlinear analysis formulation > Inelastic stress-strain behavior

Flow rule relates plastic strain increments to stress increments after onset of initial yielding. We define a plastic potential Q, which has units of stress and is a function of stresses, . The plastic strain increments (flow rule) are given by:

(138)

where dλ represents a scalar that may be called a "plastic multiplier". Thus:

p_57_image010

(139)

This rule is known as the normality principle because the above relations can be interpreted as requiring the normality of the plastic strain increment vector to the yield surface in the hyper-space of stress dimensions.

The flow rule is called "associated" if Q=F and "non-associated" otherwise. Associated flow rules are commonly used for ductile metals, but non-associated rules are better suited to model soil and granular materials.

p_58_image003

Fig. 39. (a) Geometrical representation of the plastic strain increment; (b) normality rule in 2D stress-space.