PSI - Issue 41

Daniele Gaetano et al. / Procedia Structural Integrity 41 (2022) 439–451 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Advanced composite materials are known to exhibit superior mechanical behaviors compared to conventional construction materials, especially in terms of strength and toughness properties. Their exceptional capability to carry external loads of both static and dynamic types is essentially due to their peculiar microstructural configuration, usually arising from the combination of a soft matrix and continuous/discontinuous reinforcements in the form of fibers, particles, platelets with different aspect ratios and sizes, ranging from nano- to micro-scales. Therefore, such materials are widely used in many applications of building and civil engineering, as in the seismic retrofitting of existing constructions. Despite these exceptional mechanical performances, advanced composite materials are typically affected by different kinds of damage mechanisms, such as matrix cracking, debonding between matrix and reinforcements, fiber breakage, delamination, fiber kinking, and buckling, which are not experienced by more traditional materials. Such damage mechanisms, which initially take place at the microscopic level, may strongly interact with each other, thus influencing the overall mechanical behavior of these materials (see, for instance, Luciano and Barbero (1995), Luciano and Willis (2005), Tabiei and Zhang (2018), Greco et al. (2020b), Greco et al. (2021a), Pranno et al. (2022)). Among them, laminated composites, which have been used for several years for the structural retrofit of existing constructions, are usually subjected to both intra- and inter-ply failure mechanisms, which can also interact to each other, thus negatively affecting their overall structural performances (see, for instance, Lonetti et al. (2003), Yao and Tend (2007), Bruno et al. (2016a)). In order to take into account accurately all the potential failure mechanisms in such materials, fully microscopic problems should be formulated and subsequently solved, being able to provide a complete description of all the underlying microstructural details as well as of their evolution (see, for instance, Wittel et al. (2003), Sheng et al. (2010), Pepe et al. (2020)). Nevertheless, the related numerical simulations would be unpractical due to the resulting huge computational effort, so that more efficient approaches are usually required for real-life engineering applications. In particular, two alternative classes of models have been extensively used to define accurate material behaviors for complex microstructures, i.e., phenomenological models and micromechanical models. On the one hand, several phenomenological models have been developed for isotropic materials, especially in the context of Continuum Damage Mechanics (CDM), and subsequently adapted to the anisotropic case of general composite materials (see, for instance, Ladeveze and LeDantec (1992), Boubakar et al. (2002)). According to these models, the effects of micro-cracks on the material response at the macroscopic scale are taken into account via the introduction of several damage state variables associated with the reduction of the material stiffness along different directions. Such an approach inevitably leads to notable difficulties regarding the identification of a great number of associated material parameters. On the other hand, micromechanical models have been introduced to overcome the aforementioned limitation of purely phenomenological ones. The main concept underlying this approach is to predict the overall mechanical response of heterogeneous materials starting from the properties of the different individual microscopic constituents, which are supposed to be known, by establishing either analytical or numerical relationships between the microscopic and the macroscopic fields (Miehe et al. (2002), Massart et al. (2004), Hain and Wriggers (2008), Barretta et al. (2015), Otero et al. (2015), Greco et al. (2018)). Many of such micromechanical models have been widely used within the more general framework of multiscale strategies (Greco et al. (2014), Matouš et al. (2017), Leonetti et al. (2018), Greco et al. (2020a), Oskay et al. (2020)). It is well known that classical micromechanical approaches, being based on first-order homogenization schemes, are not suitable for investigating the nonlinear response of composite materials in the presence of strain localization phenomena. In fact, such homogenization schemes cannot correctly capture softening behaviors, due to the ill posedness of the macroscopic boundary value problem defined on a properly identified Representative Volume Element (RVE), as shown by Gitman et al. (2007). From the numerical point of view, this issue is revealed through a pathological mesh dependency of the (macroscopic) mechanical response of the equivalent homogenized material. In order to overcome the limitations of classical approaches, refined homogenization schemes have been proposed in the recent years, including higher-order homogenization (Kouznetsova et al. (2004)), coupled-volume homogenization (Gitman et al. (2008)), energy-based regularized homogenization (Petracca et al., 2016), micropolar homogenization (de Borst (1991), Trovalusci et al. (2014), Trovalusci et al. (2015)), and continuous-discontinuous