Issue 30

D. Tumino et alii, Frattura ed Integrità Strutturale, 30 (2014) 317-326; DOI: 10.3221/IGF-ESIS.30.39 318 consideration for composite sandwich panels, both as primary and secondary structures, has been growing in particular in the transport sector [3,4]. This is for instance witnessed by the many recent EU funded projects that have somewhat involved the development of sandwich solutions, some of which comprise: ALCAS, APOLISS, CELPACT, DE-LIGHT, ENLIGHT, HYCOPROD, LITEBUS, MID-MOD, SANDWICH, SANDCORE, [3, 5]. A limitation to this high demand of sandwich solutions, and their more widespread adoption, is the lack of an adequate mechanical characterisation and specific design tools [3]. Furthermore, a composite sandwich is subjected to typical damaging of monolythic composites like delamination and debonding of laminated costituents [6-9]. The present study has considered a “structured core” sandwich concept, in which the traditional foam or honeycomb core is replaced or assisted by a corrugated laminate, in general made of the same material of the skin faces (see Fig. 1). Corrugated-core sandwich concepts with various geometries (the most recurring being the trapezoidal and the sinusoidal shapes) have been proposed since the beginning of the last century [10]. Applications have been for many years limited to whole metallic or cardboard structures, and the extension to fully FRP solutions dates around the end of last century [11- 13]. One reason for the special appeal of this class of sandwiches is the improved in-plane crashworthiness and out of plane impact resistance, mainly obtained by the more difficult skin-core debonding due to the generally stronger joining between the corrugated core and the skin faces [14-16]. The behaviour of corrugated sandwiches under transverse concentrated loading, typically poor for traditional foam cored sandwiches, is also significantly improved in many aspects: local indentation, local skin buckling, out-of-plane shear resistance [17,18]. Finally, the overall in plane stiffness and strength performances, especially in the corrugation direction, are also significantly improved. These advantages usually come at the expenses of a weight penalty (densities of corrugated cores are generally higher than foam cores), and a more complex manufacturing assembly. Another difficulty intrinsic to the adoption of corrugated core sandwiches has been the lack of analytical/numerical tools for the effective prediction of their mechanical response at large scales, essential for designing complex structures (e.g. ships, aircrafts, heavy mass transport structures, etc..). In these cases, a detailed 3D FEM representation of the material is obviously far too computationally onerous and time consuming. By considering the periodic nature of the corrugation pattern, a number of works have tackled the problem by trying to homogenise the sandwich material into an equivalent two-dimensional orthotropic continuum material [10]. A structural sub-element of material is first identified as the repeating unit. The mechanical response of this elementary cell, subject to some kinematic conditions, is then reproduced by finding the elastic constants of a continuum plate element able to determine an equivalent response in terms of forces or energies. In general a simplified Kirchoff-Love plate behaviour is assumed (classical sandwich laminate theory), modified to allow for transverse shear deformation (Reisner-Midlin plate model). In fact the intrinsic out-of-plane low shear rigidity in sandwiches requires this further modelling effort [19,20]. One of the first homogenisation models, for a corrugated trapezoidal core shape, was proposed by Libove et al [21,22]. In these seminal works, some simplifying assumptions are made on the strain behaviour of the corrugated sandwich, such as infinite out-of-plane rigidity (no local indentation and skin face buckling can then be modelled), and transverse sections remaining straight in the deformed configuration, although allowed to rotate with respect to the middle plane (accounting for first order transverse shear deformation). It is noticed that the method outlined in [21,22] considers isotropic material constituents, although the final homogenised element is orthotropic due to the unidirectional orientation of the corrugation (structural ortotropy). Following the above-described general approach, several other more or less refined homogeneisation methods have been proposed [10]. A number of works have extended the Libove’s approach to different corrugations, obtaining some closed- form analytical solutions for specific geometries [23-28]. Some other works have proposed a characterisation of the homogenised element by FEM simulation of the behaviour of the corrugated sandwich elementary cell [29,30]. A number of works have proposed a plate formulation based on the Classical Lamination Theory [27,31,32], in some cases considering the corrugation as a separate layer from the faces [33]. A few authors have dedicated special effort to improve the modelling of the transverse shear deformation behaviour [34-36]. Another more sophisticated analytical approach, still based on the possibility to identify an elementary repeating element of material, is also the “asymptotic expansion homogenisation”, successfully extended to corrugated sandwiches by a number of authors [10,37]. In the present work the classic approach presented by Libove et al [21,22] is revised in order to extend it to the use of orthotropic constituent materials. This in order to obtain an homogenisation model for a fully composite corrugated sandwich, where both skin faces and corrugated sheets are made of an orthotropic Glass Reinforce Polymer (GRP) material. The core laminate is in particular corrugated along one direction, and presents a trapezoidal shape type geometry with wide crests and troughs that provide the sites for the attachment to the skin faces, realised by a chemical bonding