Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29 387 systems with mid-thickness cracks (  =1) and in systems where the crack is only slightly misaligned, down to  =0.8. In highly asymmetric systems, the connection modulus matching the elasticity solutions appears not to be unique and depends on the elementary loading conditions. The differences are due to the limitations of the structural model, which neglects mutual coupling effects due to the deformations of adjacent points along the longitudinal axis (Winkler type support). In these problems, the matching coefficient to determine the a priori unknown model parameter should be chosen based on the role played by each compliance coefficient in the problem of interest. As an example, in a fracture mechanics problem devoted to the evaluation of the energy release rate, the fact that the contribution of the root rotations due to crack tip moments always prevails on that of the shear forces, since it varies as a higher power of the crack length, could suggest to choose the root rotation under symmetrical bending as matching coefficient. Results also show that the model of two Timoshenko beams connected by a Winkler type bond accurately defines the root displacement coefficients of symmetric fracture specimens under general loading conditions and overcome the limitations of models based on Euler-Bernoulli beam theory, which largely overestimate predictions of these coefficients. On the other hand, the simplicity of the closed form solutions of the Euler-Bernoulli model, where the correction factor is independent of the material orthotropy and simple rescaling formulas can be used to define root coefficients, suggests the use of these solutions for all problems where the effects of the root displacements are negligible compared to the other root deformations. A CKNOWLEDGEMENTS he authors acknowledge support by the Italian Department for University and Scientific and Technological Research (MURST) in the framework of the research MIUR Prin15 project number 2015LYYXA8 "Multi-scale mechanical models for the design and optimization of micro-structured smart materials and metamaterials", coordinated by professor A. Corigliano. RM acknowledges support by the U.S. Navy, Office of Naval Research, grant N00014-17-1-2914. R EFERENCES [1] Wang, J., Qiao, P. (2004). Interface crack between two shear deformable elastic layers, J. Mech. Phys. Solids, 52, pp. 891-905. [2] Li, S., Wang, J., Thouless, M.D. (2004). The effects of shear on delamination in layered materials, J. Mech. Phys. Solids, 52(1), pp. 193-214. [3] Andrews, M.G., Massabò, R. (2007). The effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, Eng. Fracture Mech., 74, pp. 2700-2720. [4] Pandey, R.K., Sun, C.T. (1996). Calculating strain energy release rate in cracked orthotropic beams, J. Thermoplast. Compos. Mater., 9(4), pp. 381-395. [5] Yu, H.-H., Hutchinson, J.W. (2002). Influence of substrate compliance on buckling delamination of thin films, Int. J. Fracture, 113, pp. 39-55. [6] Salganik, R.L., Ustinov, K.B. (2012). Deformation problem for an elastically fixed plate modeling a coating partially delaminated from the substrate (Plane Strain), Mech. Solids, 47, pp. 415–425. [7] Ustinov, K.B. (2015). On influence of substrate compliance on delamination and buckling of coatings, Eng. Failure Analysis, 47 (PB), pp. 338-344. [8] Suo, Z. (1990). Delamination specimens for orthotropic materials, J. Appl. Mech., 57, pp. 627-634. [9] Brandinelli, L., Massabò, R. (2006). Mode II Weight Functions for isotropic and orthotropic Double Cantilever Beams, Int. J. Fracture, 139(1), pp. 1-25. DOI: 10.1007/s10704-006-6358-0. [10] Thouless, M.D. (2018). Shear forces, root rotations, phase angles and delamination of layered materials, Eng. Fracture Mech., 191, pp. 153-167. [11] Ustinov, K., Massabò, R., Lisovenko, D. (2020). Orthotropic strip with central semi-infininite crack under arbitrary loads applied far apart from the crack tip. Analytical solution, Eng. Failure Analysis, 110, 104410. DOI: 10.1016/j.engfailanal.2020.104410. [12] Ustinov, K.B. (2019). On semi-infinite interface crack in bi-material elastic layer, European J. Mech./A Solids, 75, pp. 56-69. T