Page 267 - Marine Structural Design

Chapter I2 A Theoiy of Nonlinear Finite Element Analysis 243

112
+-(Ay;' + Ay$ tdyij]
3
2
If the plastic strain increment in uniaxial loading in x direction is defined as A&,' , and the
condition for incompressibility of plastic strain
A&,' + A&yP +At$' = 0 (A.20)

is used, the following equation may be obtained.
A&,'
A&yP =A&: =-- Arc = Arc = Ayg = 0 (A.21)
2'
Substituting Eq.(A.21) into Eq. (A.19), we obtain,

-P
A& =A&: (A.22)
This means that the increment of equivalent plastic strain is a conversion of the plastic strain
increment in multi-axial stress condition to that of the uniaxial stress condition.
The plastic strain increment may be obtained from the flow rule. If the plastic potential is
defined as yield function5 the plastic strain increment is expressed as,

(A.23)

where, yield function f is expressed in Eq. (A. 17). AR (:BO) is a undetermined scalar constant,
and {c' f is a vector of deviatoric stress as below,

=
(01) (A.24)

Eq. (A.24) means that the plastic strain increment is in the perpendicular direction of yield
surface, f=O as shown in Figure A.6.