Flow Rule and Incremental Constitutive Law

Let g be a scalar function such that the plastic strain increment de can be obtained as follows  

This is referred to as the ow rule of plasticity. The parameter A is determined by the hardening law (mentioned later). 

The flow rule (2.302) implies that the direction of the plastic strain increment deP is normal to the surface g = constant, and coincides with the stress a. For isotropic materials this can be described as follows. We introduce the unit tensors (see Sect. 2.8.3) as 

These are orthonormal as described in Sect. 2.8.3, which gives 

Therefore the direction of deP coincides with the direction of the global stress a if the material is isotropic. 

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