<CRITERION> karafillis_boyce#

Description#

Also known as the K-B criterion, the karafillis-boyce criterion was developed in 1993 at MIT. This criterion is constructed by mixing two yield functions \(\phi_1\) and \(\phi_2\). As shown in the equations below \(\phi_1\) represents a yield locus located between the Von Mises yield locus and the Tresca yield locus and \(\phi_2\) varies from von Mises to a theoretical upper bound as \(m\) changes from \(2\) to \(\infty\).

(352)#\[{\phi} = \left(1-c\right)\phi_1 +c\phi_2 = 2 Y^m\]

where

(353)#\[\begin{split}\begin{aligned} &\phi_1 = \left| S_1 - S_2 \right|^m + \left| S_2 - S_3 \right|^m + \left| S_3 - S_1 \right|^m \\ &\phi_2 = \frac{3^m}{2^m-1 + 1}\left( \left| S_1 \right|^m + \left| S_2 \right|^m + \left| S_3 \right|^m \right) \\ \end{aligned}\end{split}\]

and \(S_i\) are the principal values of the isotropic plasticity equivalent(IPE) stress tensor as defined below, \(Y\) is the average yield stress in uniaxial tension, and \(L\) is a fourth order tensorial operator which introduces material anisotropy.

(354)#\[{\ten S} = \tenf L \left(\ten \sigma - \ten B \right)\]

Syntax#

The basic input sytax here is:

*criterion karafillis_boyce \(~\,\) coefficients c1, c2, c3 c4, c5, c6.

Example#

*criterion karafillis_boyce
   m  2.0
   c  0.0
   c1 1.0
   c2 1.0
   c3 1.0
   c4 1.0
   c5 1.0
   c6 1.0