Hierarchical heterogeneous one-dimensional problem in linear viscoelastic media

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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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
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
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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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
308255The SofTMech Statistical Emulation and Translation HubDirk HusmeierEngineering and Physical Sciences Research Council (EPSRC)EP/T017899/1M&S - Statistics