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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1. Introduction The employment of new technologies for the manufacturing process of composite materials (Jandyal et al., 2022; Ko et al., 2019; Parmar et al., 2022), aimed at making them more versatile for various engineering applications (civil, aerospace, and mechanic), has made it possible in the last years to obtain smart materials with improved mechanical properties by appropriately tailoring their microstructure. These kinds of materials, known in technical literature as metamaterials (Liu and Zhang, 2011; Wu et al., 2019), have the particular feature of owning specific properties due to their individual structure rather than their chemical composition. Their properties are designed by manipulating their physical structure, even incorporating multiple properties by matching different characteristics, e.g. mechanical and electrical properties (Barchiesi et al., 2019; Sihvola, 2007; Surjadi et al., 2019). This not only makes them significantly different from natural materials but also contributes to the extreme interest of the scientific and industrial communities in their potential applications (Valipour et al., 2022). Alongside the analysis of their structural shapes and mechanical properties, it is a fundamental issue to study the potential collapse mechanisms that can arise in metamaterials’ microstructure, especially when large deformations are involved. Among these failure phenomena, that occur at multiple scales, fracture, decohesion, instability, and compression-induced contact are the ones to focus on (De Maio et al., 2024b, 2024a; Orifici et al., 2008; Segurado and LLorca, 2005). Further attention should also be paid to the dynamic behaviour of these types of materials in order to study how wave propagation occurs when periodic microstructures are adopted (Burlon and Failla, 2023; De Maio et al., 2024c; Galich et al., 2017; Pranno et al., 2022). Therefore, the necessity to analyse multiple collapse mechanisms, which may also interact with each other, has led researchers to focus on developing advanced numerical models suitable for this purpose in recent years. Out of these numerical methods, multiscale approaches (Greco et al., 2014; Temizer and Wriggers, 2011) and non-linear homogenization techniques (Bruno et al., 2014; Michel et al., 2010), developed in a finite deformation setting, have been widely used, due to the capability of combining the accuracy of the results and computational efficiency. Among the technical literature, several works that employed multiscale approaches or non linear homogenization schemes, analyse the effects of the instability phenomena in periodic composites. For instance, the early works of (Triantafyllidis and Maker, 1985) and (Geymonat et al., 1993) studied the micro- and macroscopic instabilities in hyperelastic composite characterized by a periodic microstructure, and the correlation between each other (De Maio et al., 2023). More recently, instead, (Cricr ı̀ and Luciano, 2013) analysed the effects of instability in a finite homogenization setting, assuming a nonlinear behaviour for the constituents. (Nezamabadi et al., 2009) proposed a multilevel strategy for heterogeneous materials in which instabilities may arise when buckling occurs at micro- and macroscopic scales. The effects of the fiber micro-buckling in unidirectional fiber-reinforced composites are also studied in (Bigoni et al., 1997; Nezamabadi et al., 2015), proving that such a phenomenon can lead to a reduction in compressive strength as the microcracks increase (Greco et al., 2024), similar to that experienced by structural elements reinforced using composites (Allix and Corigliano, 1999; Lignon et al., 2013). Regarding the hyperplastic materials, analysed in the present work, the first studies on the buckling-induced instability of these materials subjected to compressive loads have been developed by (Triantafyllidis and Maker, 1985). Furthermore, in (Nestorović and Triantafyllidis, 2004) the authors investigated the influence of the load orientation, considering combined normal and shear loading conditions. However, both previous works neglected the effects of fracture phenomena and how they interact with instability, which could affect the whole behaviour of the microstructures. To this end, this work proposes a novel theory based on a nonlinear homogenization scheme to analyse the failure behaviour of periodic reinforced hyperelastic composites, when decohesion between the two phases (matrix and reinforcement), as well as contact and microscopic instabilities, are taken into account. For this purpose, an enhanced cohesive/contact formulation in a finite strain setting has been employed for both debonding and contact phenomena. Moreover, a combined compression-shear macro-deformation loading path is considered for the composite. The proposed numerical formulation has been implemented in the commercial finite element software COMSOL Multiphysics for characterizing the failure behaviour of 2D layered composites. The numerical results show the way in which the critical load is affected due to micro buckling phenomena by considering the interaction that occurs from contact and microscopic instabilities.