13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- In thick composite structures under flexural loading such as in ship hulls, failure is more likely to occur under a mixed-mode situation. Therefore, a formulation for interface elements having zero thickness should include a mixed-mode damage model, which, in this case, is an extension of the pure mode model. Damage initiation may be predicted by using the following criterion [8, 11]: , , 2 2 ( ) ( ) 1 I II u I u II σ σ σ σ + = if 0 Iσ > (12) , II u II σ σ = if 0 Iσ ≤ where ,u I σ , ,u II σ represent the ultimate normal and shear stresses, respectively and it is assumed that normal compressive stress does not induce damage. Providing an equivalent mixed-mode displacement: 2 2 e I II δ δ δ = + (13) and a mixed-mode ratio: II I δ β δ = (14) and taking into considering Eq. (8), we have from Eq. (12): , , 2 2 , , ( ) ( ) 1 om I om II o I o II δ δ δ δ + = (15) where , ( , ) om i i I II δ = are the relative displacements at damage initiation, which correspond to the critical interface stresses , um i σ . Combining Equations (13)-(15), the value of the equivalent mixed-mode displacement leading to damage initiation ( ) omδ results:
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