FcrIf 0Eq

where /(<7,;) is a function of stress. For example, for an isotropic incompressible material, a suitable form of this expression is:

where d is the yield strength of the material in uniaxial tension and (Te is the von Mises effective stress, given by:

In principal plane-stress space,

2 SVSU

Fig. 6 Schematic of yield surface in plane-stress space, showing strain increment vector normal to the yield surface

Equation 9 then represents the von Mises ellipse shown in Fig. 6. Iff < 0, the material response is elastic, and iff = 0 (i.e., if the stress state is on the yield surface), the material is able to deform plastically. The increments of plastic strain at yield are related through the associated flow rule:

where Ais a plastic multiplier. This equation simply states that the strain increment vector is normal to the yield surface in stress space. Additional information is needed to determine the exact value of A.

For the yield condition of Eq 7,

Now,

Also,

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