Abstract
In the present work we embrace a three scales asymptotic homogenization approach to investigate the effective behavior of hierarchical linear elastic composites reinforced by cylindrical, uniaxially aligned fibers and possessing a periodic structure at each hierarchical level of organization. We present our novel results assuming isotropy of the constituents and focusing on the effective out-of-plane shear modulus, which is computed exploiting the solution of the arising anti-plane problems. The latter are solved semi-analytically by means of complex variables and successfully benchmarked against the results obtained by finite elements. Our findings can pave the way for multiscale modeling of complex hierarchical materials (such as bone and tendons) at a negligible computational cost.
Highlights
Multiscale composites organized across two or more length scales are often encountered in nature, as well as in artificial materials designed to optimize specific properties
In the present work we apply the three-scale asymptotic homogenization developed in [25] to investigate the effective behavior of fibrous hierarchical composites
The approach permits the study of problems where several length scales are present
Summary
Multiscale composites organized across two or more length scales are often encountered in nature, as well as in artificial materials designed to optimize specific properties (see, e.g., [10]). It can provide a deeper understanding on how to modify the microstructural arrangement of the finer scales constituents to achieve the optimal design of artificial constructs (e.g. biomimetic materials). In the present work we apply the three-scale asymptotic homogenization developed in [25] (which is therein applied to hierarchical layered materials) to investigate the effective behavior of fibrous hierarchical composites. We apply the latter to find the effective out-of-plane shear of a hierarchical linear elastic reinforced composite assuming a square-like arrangement of uniaxially aligned cylindrical fibers at all hierarchical levels of organization. We conclude the manuscript (cf. Sect. 6) highlighting possible applications to realistic scenarios of interest, such as hierarchical modeling of fibril bundles and/or fusing mineral crystals as analyzed for example in [22] in the context of aged bone modeling
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