Investigation of Microscopic Instabilities in Fiber-Reinforced Composite Materials by Using Multiscale Modeling Strategies

Abstract

Fiber micro-buckling is a frequent failure mode in fiber-reinforced composite materials subjected to prevalent compression along the fiber direction. Indeed, this failure mode may lead to a sensible decrease in their strength, especially if subjected to multi-axial loading conditions, inducing also micro-crack initiation and propagation, which ultimately cause their premature collapse. Several studies have shown that instability phenomena in composite materials must be studied at both micro- and macro-scales, in order to capture all possible instability modes. It follows that a detailed model is usually required, resulting in a huge time of the related simulations. To increase the computational efficiency, different multiscale strategies have been proposed in the literature, which are able to overcome the limitations of first-order homogenization schemes, implicitly assuming well-separated spatial scales and periodic arrangement of failure mechanisms. In this work, the efficacy of two multiscale models for the instability-induced failure analysis of composite materials is investigated, with special reference to locally periodic microstructures under large deformations, for which the micro-to-macro scale length ratio is much larger than zero. The first multiscale model is a semi-concurrent model, by which the macroscopic constitutive response is computed “on the fly”, whereas the latter one is a hybrid hierarchical/concurrent model, based on a multi-level domain decomposition method, according to which a numerical homogenization scheme is used only for the regions not directly influenced by local failures. Finally, the numerical accuracy of such multiscale models is assessed via comparisons with direct simulations, also highlighting the role of boundary effects on the overall structural response.