Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29 384 0 0 1 (1 ) V V EB s xz d d                 (26) which is a generalization of Eqn. (B.4) introduced for matching. The difference is made clear by referring to how the effects of shear deformations are accounted for in the two formulations. Within the Timoshenko beam theory, the effects of the shear deformations are taken into account through the beam compatibility and constitutive equations leading to Eqn. (2) which governs the problem and, as a consequence, they enter directly in the expressions of rotations and displacements. On the other hand, in the simplified formulation based on the Euler-Bernoulli beam theory the effects of shear deformations are included only in the matching procedure for the evaluation of the correction factor EB w k , as discussed in Appendix B. This point is discussed again in the next section with reference to a practical application of the two formulations to the analysis of an exemplary fracture specimen, since it has important effects on the determination of the root displacement compliance coefficients. Figure 11: Relative deflection compliance coefficients under a pair of longitudinal forces according to the simplified model and for degenerate orthotropic materials (  =1) with varying  =0.5,1. The final comment regards the solutions for orthotropic specimens. The correction factors obtained using the Euler- Bernoulli model EB w k are independent of the orthotropy ratio  in all cases. This sets simple rescaling rules for the compliance coefficients in Eqn. (25) and values for  ≠ 1 can be easily obtained by rescaling the values for  =1 by   1/4 for 0 M EB d and 0 N EB d , by   1/2 for 0 0 V M EB EB d c  and 0 N EB c and by   3/4 0 V EB c . On the other hand, the correction factors obtained using the Timoshenko model depend on all the elastic constants and the rescaling rules on the compliance coefficients in Eqns. (18)-(24) are more complicated, but for 0 M d and 0 N d which are independent of the Poisson ratios and rescale as   1/4 . To conclude, all compliance coefficients depend also on the second orthotropy ratio  , however the effect of  is only quantitative and does not modify the conclusions drawn above. A PPLICATION OF THE RESULTS his section presents an application of the two formulations developed in the paper to the analysis of an exemplary fracture specimen. This allows to clarify how the described results can be effectively used in practice and the differences between the two formulations. The exemplary case of the symmetric DCB specimen shown in Fig. 12a is considered. The material is linearly elastic and orthotropic with principal material directions x , y , z and longitudinal Young's modulus E x , transverse Young's modulus