Nonlinear analysis formulation > Incremental stress-strain relations

We will assume that strain increments include elastic components and plastic components and they are small. An incremental stress-strain 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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