PSI - Issue 66

Domenico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 320–330 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Keywords: Continuous/discontinuous multiscale models; homogenized damage models; cohesive crack propagation; anisotropic composite structures

1. Introduction In recent years, there has been an increasing interest in developing multi-purpose, lightweight and high performance composite materials for use in several engineering applications. Such materials possess exceptional mechanical properties and additional functionalities that result from their complex hierarchical structures at smaller scales (Llorca et al. (2011), Kadic et al. (2019), Ichihara and Ueda (2023)). Some of these innovative materials, referred to as metamaterials, can change shape in response to stresses, control the direction of waves, and adjust their stiffness and energy absorption properties (Bertoldi et al. (2017), Li et al. (2018), De Maio et al. (2023)). Given the above-mentioned features, many mechanical metamaterials are usually anisotropic heterogeneous materials even in their linearly elastic range, due to the peculiar geometric arrangements of their microconstituents. Moreover, the anisotropy level of such microstructures is further increased in the presence of nonlinear phenomena related to damage/fracture nucleation and propagation, such as matrix cracking and fiber/matrix debonding (Huang and Talreja (2006), Heeráez et al. (2015)). In this context, several homogenization and other multiscale techniques have shown their potential as a robust and reliable tool for predicting the highly anisotropic mechanical behavior of a wide variety of structural components made of composite materials (Ghosh et al. (2001), Feyel (2003), Kouznetsova et al. (2004), Massart et al. (2007), Belytschko et al. (2008), Gitman et al. (2008), Smyshlyaev (2009), Verhoosel et al. (2010), Llorca et al. (2011), Nguyen et al. (2011), Coenen et al. (2012), Greco et al. (2014), Trovalusci et al. (2015), Turteltaub et al. (2018), Yvonnet et al. (2020), Kim et al. (2020), Firooz et al. (2021), Fantuzzi et al. (2022), Pingaro et al. (2023)). However, classical multiscale approaches relying on first-order bulk homogenization schemes are no longer valid when strain localization phenomena occur, since the resulting macroscopic boundary value problem becomes ill posed. From a numerical point of view, such an ill-posedness is highlighted by a pathological sensitivity of the overall stress-strain response on the size of the Representative Volume Element (RVE) adopted for homogenization. To overcome this limitation, enhanced numerical strategies have been developed in recent years, including multiscale approaches based on second-order homogenization (Kouznetsova et al. (2004), Yvonnet et al. (2020)), micropolar homogenization (Trovalusci et al. (2015), Fantuzzi et al. (2022)), coupled-volume homogenization (Gitman et al. (2008)), and combined continuous/discontinuous homogenization (Massart et al. (2007), Belytschko et al. (2008), Verhoosel et al. (2010), Nguyen et al. (2011), Coenen et al. (2012), Turteltaub et al. (2018)), most of which have been devoted to investigating damage evolution in heterogeneous structures. Many of these strategies have been developed in the framework of the so-called FE 2 -like methods, for which a microscopic finite element model needs to be solved for each integration point of the macroscopic finite element model (see Feyel (2003) for additional details). In this case, the related numerical computations are too time consuming for real-life engineering applications, especially in the presence of highly nonlinear mechanical behaviors. In the present work, a novel combined continuous/discontinuous multiscale approach is proposed for damaging anisotropic composite structures, which relies on a cohesive/bulk homogenization method, to be used in conjunction with a Diffuse Interface Model (DIM), already adopted by some of the present authors for the prediction of multiple cracking in concrete and other construction materials (see, for instance, Greco et al. (2020), Gaetano et al. (2022a), Gaetano et al. (2022b), Greco et al. (2022), Pascuzzo et al. (2022b), Greco et al. (2024)). The key ingredient of the proposed approach is a numerical procedure conceived to extract “on-the-fly”, i.e. , during the macroscale computations, the softening part of homogenized stress-strain law computed for the bulk via standard hierarchical homogenization, and to project it on the interface, with the final aim of obtaining the overall Traction-Separation Law (TSL) of cohesive interfaces embedded in the macroscopic computational mesh. The main advantage of the proposed cohesive/bulk hierarchical multiscale technique over FE 2 -like computational homogenization approaches is that a micromechanically based TSL is derived through online computations in a very efficient manner, without resorting to the solution of a new microscopic boundary value problem defined for the cohesive interfaces.