Cruz-González, O.L., Ramírez-Torres, A. , Rodríguez-Ramos, R., Penta, R. and Lebon, F. (2022) Hierarchical heterogeneous one-dimensional problem in linear viscoelastic media. European Journal of Mechanics - A/Solids, 95, 104617. (doi: 10.1016/j.euromechsol.2022.104617)
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Abstract
We address the homogenization of a linear viscoelastic and hierarchical composite material in a one-dimensional (1D) framework via a three-scale asymptotic homogenization method. We consider a family of heterogeneous problems with periodic, rapidly-oscillating and piece-wise coefficients that model a structure with two hierarchical levels of organization. Here, we assume continuity contact conditions at the interfaces among the constituents and set a straightforward geometrical configuration in order to gain a better insight of the multiscale problem. The main goal is to provide a general overview of the procedure and validate the approach by means of a comparison between the solution of the original heterogeneous problem, the homogenized problem and the formal asymptotic solution. In addition, we show that the three scale approach presents a clear improvement over the recursive two-scale one, and we illustrate the convergence of the solutions towards the solution of the homogenized problem when both asymptotic parameters are approaching to zero.
Item Type: | Articles |
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Status: | Published |
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., and Lebon, F. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | European Journal of Mechanics - A/Solids |
Publisher: | Elsevier |
ISSN: | 0997-7538 |
ISSN (Online): | 1873-7285 |
Published Online: | 20 April 2022 |
Copyright Holders: | Copyright © 2022 The Authors |
First Published: | First published in European Journal of Mechanics - A/Solids 95: 104617 |
Publisher Policy: | Reproduced under a Creative Commons License |
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