Incremental stressstrain relations
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We will assume that strain increments include elastic components and plastic components and they are small. An incremental stressstrain relation, analogous to the relation of elasticity can be formulated.
During an increment of plastic straining dF=0 thus:

(141) 
By substitution:

(142) 
The resulting equation to solve for the plastic multiplier dλ is:

(143) 
where Pλ is the row matrix in which both work hardening and strain hardening are included in this expression:

(144) 
Rearranging the terms yield:

(145) 
where I is a unit matrix and Eep is the generalized tangent constitutive matrix. If Q=F (associated flow rule) this matrix Eep is symmetric. For F<0 (yield has not occur) or F=0 and dF<0 (unloading from plastic state) then Eep=E.
The tangent stiffness matrix kt is now given by:

(146) 

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