Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach

Ramírez-Torres, A. , Penta, R. , Rodríguez-Ramos, R. and Grillo, A. (2019) Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach. Mathematics and Mechanics of Solids, 24(11), pp. 3554-3574. (doi: 10.1177/1081286519847687)

195989.pdf - Accepted Version



The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. During the past decades, the multiscale asymptotic homogenization technique has shown its potential in the description of such composites by taking advantage of their characteristics at the smaller scales, ciphered in the so-called effective coefficients. Here, we extend previous works by studying the in-plane and out-of-plane effective properties of hierarchical linear elastic solid composites via a three-scale asymptotic homogenization technique. In particular, the approach is adjusted for a multiscale composite with a square-symmetric arrangement of uniaxially aligned cylindrical fibers, and the formulae for computing its effective properties are provided. Finally, we show the potential of the proposed asymptotic homogenization procedure by modeling the effective properties of musculoskeletal mineralized tissues, and we compare the results with theoretical and experimental data for bone and tendon tissues.

Item Type:Articles
Additional Information:ART gratefully acknowledges the research project ‘Mathematical multi-scale modeling of biological tissues’ (N. 64) financed by the Politecnico di Torino (Scientific Advisor: Alfio Grillo). ART and AG acknowledge the Dipartimento di Scienze Matematiche (DISMA) ‘G.L. Lagrange’ of the Politecnico di Torino, ‘Dipartimento di Eccellenza 2018–2022’ (Department of Excellence 2018–2022). RRR acknowledges the funding of Proyecto Nacional de Ciencias Básicas 2016–2018 (Project No. 7515) and Departamento de Matemáticas y Mecánica, IIMAS and PREI-DGAPA at UNAM.
Glasgow Author(s) Enlighten ID:Penta, Dr Raimondo and Ramirez Torres, Dr Ariel
Authors: Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., and Grillo, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematics and Mechanics of Solids
ISSN (Online):1741-3028
Published Online:25 May 2019
Copyright Holders:Copyright The Author(s) 2019
First Published:First published in Mathematics and Mechanics of Solids 24(11):3554-3574
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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