Initial strain method
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In this method the material is allowed to sustain stresses outside the failure criterion for finite "periods". Instead of plastic strains, we refer to viscoplastic strains and are generated as a rate that is related to the amount by which yield has been violated by:

(163) 
where F is the yield function and Q is the plastic potential function.
The increment of viscoplastic strain, which is accumulated from one iteration to the next, is obtained through multiplication the strain rate by a pseudo time step as:

(164) 
and

(165) 
where the time step for numerical stability depends on the assumed failure criterion as:

for VonMisees materials 
(166) 

for MohrCoulomb materials 
(167) 
The derivatives of the plastic potential function Q with respect to stresses are expressed as:

(168) 
where where t represents the second deviatoric stress invariant:

(169) 
and

(170) 

, etc. 
(171) 

(179) 
where the first invariant (mean stress invariant) s is given by the relation:

(180) 
It may be noted that in geotechnical applications, plane strain conditions are enforced and in the above equations .
The viscoplastic strain rate is evaluated numerically by the expression:

(181) 
where

(182) 

(183) 

(184) 

(185) 
The selfequilibrating body loads are accumulated at each time step within each load step by summing the following integrals for all yielded elements (F>0 at Gauss points):

(186) 
This process is repeated at each time step iteration until no integration point stresses violate the failure criterion within a given tolerance. The convergence criterion is based on a dimensionless measure of the amount by which the displacement increment vector Ui changes from one iteration to other.

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