Incremental stress-strain relations

<< Click to Display Table of Contents >>

Navigation:  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 p_58_image007of elasticity can be formulated.


During an increment of plastic straining dF=0 thus:







By substitution:






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






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






Rearranging the terms yield:






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:














© 2020 GeoStru Software