PSI - Issue 66

Daniele Gaetano et al. / Procedia Structural Integrity 66 (2024) 478–485 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

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4. Conclusions This work presents an innovative nonlinear homogenization framework for studying the buckling phenomena in hyperelastic composites considering the interaction between contact mechanisms and microscopic instabilities. Considering combined shear-compression loading conditions, the behaviour of a Neo-Hookean solid RVE, embedding contact and cohesive interfaces, has been analyzed. Periodic boundary conditions have been applied on the chosen RVE by prescribing the macroscopic deformation gradient via the classical macro-to-micro coupling relations. The microscopic stability analyses have been performed by monitoring the critical load factor as the percentage of the maximum mode II displacement jump increases with respect to its critical counterpart. Three different formulations for the stability functional have been proposed and employed in the proposed nonlinear homogenization framework. The percentages of variation of the simplified formulations with respect to the exact ones have been also evaluated. The numerical outcomes highlight that the critical load factor quickly dropped as the percentage of the tangential displacement jump overcame the value of 80%, for all the adopted stability functional formulations. On the other hand, for low values of the percentage of displacement jump, the critical load decreases less quickly. Furthermore, it has been noted that, for a small percentage of the tangential displacement jump, the simplified I formulation exhibits very close values with respect to the exact stability functional, with a percentage of variation less than 10%. In contrast, for formulation II, even small tangential displacement jumps induced high differences between the critical load factors of the simplified and the exact formulations. As a future perspective, parametric analyses could be performed, varying the volume fraction of the unit cell and the stiffness contrast between the two materials, in order to understand how these parameters affect the microscopic critical load factors for combined compression-shear loading conditions. Acknowledgements Fabrizio Greco and Daniele Gaetano gratefully acknowledge financial support from the Italian Ministry of Education, University and esearch ( IU ) under the P. .I.N. 2022 National Grant “Innovative tensegrity lattices and architectured metamaterials (ILA )” (Project ode 20224LB Z; University of alabria esearch Unit, UP H53D23001180006), funded by European Union – Next Generation EU under the National Recovery and Resilience Plan (NRRP), Mission M4, C2 Component- Investment 1.1. References Allix, O., Corigliano, A., 1999. Geometrical and interfacial non-linearities in the analysis of delamination in composites. International Journal of Solids and Structures 36, 2189 – 2216. https://doi.org/10.1016/S0020-7683(98)00079-1 Barchiesi, E., Spagnuolo, M., Placidi, L., 2019. Mechanical metamaterials: a state of the art. Mathematics and Mechanics of Solids 24, 212 – 234. https://doi.org/10.1177/1081286517735695 Bigoni, D., Ortiz, M., Needleman, A., 1997. Effect of interfacial compliance on bifurcation of a layer bonded to a substrate. International Journal of Solids and Structures 34, 4305 – 4326. https://doi.org/10.1016/S0020-7683(97)00025-5 Bruno, D., Greco, F., Luciano, R., Nevone Blasi, P., 2014. Nonlinear homogenized properties of defected composite materials. Computers & Structures 134, 102 – 111. https://doi.org/10.1016/j.compstruc.2013.11.018 Burlon, A., Failla, G., 2023. On the band gap formation in locally-resonant metamaterial thin-walled beams. European Journal of Mechanics - A/Solids 97, 104798. https://doi.org/10.1016/j.euromechsol.2022.104798 Cricr ı̀ , G., Luciano, R., 2013. Homogenised properties of composite materials in large deformations. Composite Structures 103, 9 – 17. https://doi.org/10.1016/j.compstruct.2013.03.015 De Maio, U., Gaetano, D., Greco, F., Luciano, R., Pranno, A., 2024a. Degradation analysis of dynamic properties for plain concrete structures under mixed-mode fracture conditions via an improved cohesive crack approach. Frattura ed Integrità Strutturale 18, 422 – 439. https://doi.org/10.3221/IGF-ESIS.68.28 De Maio, U., Greco, F., Lonetti, P., Pranno, A., 2024b. A combined ALE-cohesive fracture approach for the arbitrary crack growth analysis. Engineering Fracture Mechanics 301, 109996. https://doi.org/10.1016/j.engfracmech.2024.109996 De Maio, U., Greco, F., Luciano, R., Sgambitterra, G., Pranno, A., 2023. Microstructural design for elastic wave attenuation in 3D printed nacre like bioinspired metamaterials lightened with hollow platelets. Mechanics Research Communications 128, 104045. https://doi.org/10.1016/j.mechrescom.2023.104045 De Maio, U., Greco, F., Nevone Blasi, P., Pranno, A., Sgambitterra, G., 2024c. Elastic Wave Propagation Control in Porous and Finitely Deformed Locally Resonant Nacre-like Metamaterials. Materials 17, 705. https://doi.org/10.3390/ma17030705