A hierarchical asymptotic homogenization approach for viscoelastic composites

Cruz-González, O. L., Ramírez-Torres, A. , Rodríguez-Ramos, R., Penta, R. , Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Sabina, F. J. and Lebon, F. (2020) A hierarchical asymptotic homogenization approach for viscoelastic composites. Mechanics of Advanced Materials and Structures, (doi: 10.1080/15376494.2020.1722872) (Early Online Publication)

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Abstract

Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method. In this approach, we consider the assumption of a generalized periodicity in the different structural levels and their characterization through the so-called stratified functions. The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization by using the correspondence principle and the Laplace-Carson transform. Considering isotropic components and a perfect contact at the interfaces between the constituents, analytical solutions, in the Laplace-Carson space, are found for the local problems and the effective coefficients are computed. An interconversion procedure between the effective relaxation modulus and the effective creep compliance is carried out for obtaining information about both viscoelastic properties. The numerical inversion to the original temporal space is also performed. Finally, we exploit the potential of the approach and study the overall properties of a hierarchical viscoelastic composite structure representing the dermis.

Item Type:Articles
Keywords:Dermis, hierarchical structures, viscoelastic composites, non-aging, three-scale asymptotic homogenization method, generalized periodicity.
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Penta, Dr Raimondo and Ramirez Torres, Dr Ariel
Authors: Cruz-González, O. L., Ramírez-Torres, A., Rodríguez-Ramos, R., Penta, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Sabina, F. J., and Lebon, F.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mechanics of Advanced Materials and Structures
Publisher:Taylor and Francis
ISSN:1537-6494
ISSN (Online):1537-6532
Published Online:10 February 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Mechanics of Advanced Materials and Structures 2020
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics