Issue 50

K. Meftah et alii, Frattura ed Integrità Strutturale, 50 (2019) 276-285; DOI: 10.3221/IGF-ESIS.50.23 279 e p d d d      (10) The elastic-plastic strain increment is given by the incremental form of:   1 F d D d d          (11) where d  is a proportional constant called plastic multiplier and F    is the flow vector, which is normal to the adopted yield function, presented in Eq. (12), considering that the yield surface only depends on the magnitude of the applied principal stresses and of a hardening parameter H : ( , ) ( , ) ( ) 0 Y F H f H H       (12) where Y  is the yield stress and f (  , H ) is the yield criterion. In this paper, the elasto-plastic constitutive model based on the Von-Mises associated yield criterion is adopted for the Reissner-Mindlin plate theory [15]:     1 2 2 2 2 2 2 2 1 ( ) 6 2 xx yy xx yy xy yz zx Y f                          (13) where e  is the Von-Mises effective stress. The elastic-plastic incremental stress strain relationship:   ep e p d D d d          (14) ep e F d D d d                   (15) The differential form of Eq. (12) is: 0 Y f dF d H H           (16) or T a 0 dF d Ad      (17) in which the flow vector a T is define as: T a x y xy yz zx f f f f f f                             (18) Eqns. (16) and (17) can be reduced to get the hardening parameter A as: 1 Y A d H H       (19) The plastic rate multiplier can be obtained as: