Issue 49

M. Tashkinov et alii, Frattura ed Integrità Strutturale, 49 (2019) 396-411; DOI: 10.3221/IGF-ESIS.49.39 398 nodal displacements behind the delamination front [18]:   1 2 I I E X u Z w      , (1) where I X and I Z are shear and opening forces in the node I , u  and w  are displacements corresponding to the shear and opening in the node L (Fig. 1). Figure 1: Schematic implementation of the VCCT for finite elements The energy release rate is then calculated as: ΔE G ΔA  , (2) where ∆ is a crack surface. In real materials, the debonding crack usually grows simultaneously in all three modes of deformation (opening, in-plane shear and out-of-plane shear). In order to take this into account, the energy release rates are calculated for each mode ( , ,  ) I II III G G G and the subsequently summed: T I II III G G G G    . (3) The latter is compared with the critical value C G . In this case, the beginning of the opening of two nodes and growth of the crack occurs when the following condition is met: 1 T c G G  . (4) The critical value c G depends on all three modes of deformation and is defined using the mixed criterion. One of the most used criterion in three-dimension space is the Benzeggah and Kenane (BK) criterion [21]:   1 I II III II III IC IIC IC I II III G G G f G G G G G G G G                 , (5) where the constants Ic G , IIc G are determined experimentally for each laminated composite material.