Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29 381 Figure 5: Relative rotation compliance coefficients under symmetrical bending for degenerate orthotropic materials (  =1) with varying  =0.5,1. The three upper curves refer to  =0.5, the lower to  =1 (isotropy). Figure 6: Relative rotation compliance coefficients under a pair of longitudinal forces for degenerate orthotropic materials (  =1) with varying  =0.5,1. The three upper curves refer to  =0.5, the lower to  =1 (isotropy). In isotropic and orthotropic symmetric specimens, where  =1, all matching procedures lead to the same value of k w , as shown in Fig. 3 for isotropy. The same is true for EB w k , which differs from k w also because it does not depend on the Poisson ratios. This implies that matching a single root rotation coefficient against the 2D solutions using Timoshenko or Euler-Bernoulli beam theory yields accurate predictions of all other root rotation coefficients, through Eqns. (18), (22), (24) and (25), as shown in Figs. 4-6 and 9. As further validation of these results, Tabs. 7 and 8 of Appendix B show that for isotropic layers 0.812 EB w k  , 0 5.436 V EB d  and 0 3.659 V EB c  . These values perfectly match the results derived in [10] for a symmetrical DCB specimen. In isotropic and orthotropic asymmetric specimens, with  ≠ 1, using different root rotation coefficients in the matching procedure yields different predictions of k w or EB w k and the difference increases on decreasing  , as shown in Fig. 3 for an isotropic layer. Fig. 3 shows that the percentage difference between the k w s calculated using 0 V d and 0 M d as matching coefficient and the Timoshenko model is about 6%,7% for  =0.8 and  =0,0.3 and 23%,29% for  =0.6 and  =0,0.3. The