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Materials
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Mechanical Modeling of Viscoelastic Composite Materials
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Mechanical Modeling of Viscoelastic Composite Materials

A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Advanced Composites".

Deadline for manuscript submissions: closed (10 June 2023) | Viewed by 4125

Special Issue Editors

Prof. Dr. Frédéric Lebon

E-Mail Website
Guest Editor
CNRS, Centrale Marseille, Aix Marseille Universite, LMA UMR 7031, Marseille, France
Interests: contact mechanics; asymptotic techniques; interfaces; heterogenous materials; modelling
Special Issues, Collections and Topics in MDPI journals
Dr. Reinaldo Rodríguez-Ramos

E-Mail Website
Guest Editor
1. Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, La Habana 10400, Cuba
2. PPG-MCCT, Universidade Federal Fluminense, Av. dos Trabalhadores 420, Vila Sta. Cecília, Volta Redonda 27255-125, Brazil
Interests: composite materials; continuum mechanics; wave propagation in solids; homogeneization methods; micromechanics; biomechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, there are different types of materials characterized by a viscoelastic response, where the phases generally involve both instant elastic and time-dependent viscous behavior, as well as those with hierarchical structures found in biological contexts driven by natural evolution. Several examples consist of viscoelastic constituents which have inspired the research into synthetic composites for a variety of engineering applications with practical purposes. The present Special Issue intends to collect some theoretical and experimental approaches with the aim of achieving better performance by intentionally manipulating the complexity and inner design, and by ensuring multilength scale property control. In addition, the study of creep and relaxation behavior in viscoelasticity has gone some way towards enhancing the understanding of these kinds of composites. Viscoelastic materials are often used to improve the capability of systems to dissipate more energy, as compared to conventional materials. The mechanical properties of viscoelastic materials depend mainly on the frequency of excitations and temperature. The family of rheological models that consider the dependence of the mechanical properties of these materials on the excitation frequencies is very attractive. There are examples of several classic rheological models, such as the Zener model and the generalized Maxwell model. Moreover, the so-called fractional models, where fractional derivatives are used, can be considered relevant for the purpose of this work.

Prof. Dr. Frédéric Lebon
Prof. Dr. Reinaldo Rodríguez Ramos
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • rheological models
  • viscoelasticity
  • multiscale homogenization
  • fractional derivatives
  • multiphysics effects

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Published Papers (2 papers)

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Research

20 pages, 1120 KiB  
Article
Effective Governing Equations for Viscoelastic Composites
by Laura Miller, Ariel Ramírez-Torres, Reinaldo Rodríguez-Ramos and Raimondo Penta
Materials 2023, 16(14), 4944; https://doi.org/10.3390/ma16144944 - 11 Jul 2023
Cited by 1 | Viewed by 1755
Abstract
We derive the governing equations for the overall behaviour of linear viscoelastic composites comprising two families of elastic inclusions, subphases and/or fibres, and an incompressible Newtonian fluid interacting with the solid phases at the microscale. We assume that the distance between each of [...] Read more.
We derive the governing equations for the overall behaviour of linear viscoelastic composites comprising two families of elastic inclusions, subphases and/or fibres, and an incompressible Newtonian fluid interacting with the solid phases at the microscale. We assume that the distance between each of the subphases is very small in comparison to the length of the whole material (the macroscale). We can exploit this sharp scale separation and apply the asymptotic (periodic) homogenization method (AHM) which decouples spatial scales and leads to the derivation of the new homogenised model. It does this via upscaling the fluid–structure interaction problem that arises between the multiple elastic phases and the fluid. As we do not assume that the fluid flow is characterised by a parabolic profile, the new macroscale model, which consists of partial differential equations, is of Kelvin–Voigt viscoelastic type (rather than poroelastic). The novel model has coefficients that encode the properties of the microstructure and are to be computed by solving a single local differential fluid–structure interaction (FSI) problem where the solid and the fluid phases are all present and described by the one problem. The model reduces to the case described by Burridge and Keller (1981) when there is only one elastic phase in contact with the fluid. This model is applicable when the distance between adjacent phases is smaller than the average radius of the fluid flowing in the pores, which can be the case for various highly heterogeneous systems encountered in real-world (e.g., biological, or geological) scenarios of interest. Full article
(This article belongs to the Special Issue Mechanical Modeling of Viscoelastic Composite Materials)
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18 pages, 959 KiB  
Article
Effective Properties of Homogenised Nonlinear Viscoelastic Composites
by Alejandro Roque-Piedra, Reinaldo Rodríguez-Ramos, Raimondo Penta and Ariel Ramírez-Torres
Materials 2023, 16(11), 3974; https://doi.org/10.3390/ma16113974 - 25 May 2023
Cited by 4 | Viewed by 1797
Abstract
We develop a general approach for the computation of the effective properties of nonlinear viscoelastic composites. For this purpose, we employ the asymptotic homogenisation technique to decouple the equilibrium equation into a set of local problems. The theoretical framework is then specialised to [...] Read more.
We develop a general approach for the computation of the effective properties of nonlinear viscoelastic composites. For this purpose, we employ the asymptotic homogenisation technique to decouple the equilibrium equation into a set of local problems. The theoretical framework is then specialised to the case of a strain energy density of the Saint-Venant type, with the second Piola–Kirchhoff stress tensor also featuring a memory contribution. Within this setting, we frame our mathematical model in the case of infinitesimal displacements and employ the correspondence principle which results from the use of the Laplace transform. In doing this, we obtain the classical cell problems in asymptotic homogenisation theory for linear viscoelastic composites and look for analytical solutions of the associated anti-plane cell problems for fibre-reinforced composites. Finally, we compute the effective coefficients by specifying different types of constitutive laws for the memory terms and compare our results with available data in the scientific literature. Full article
(This article belongs to the Special Issue Mechanical Modeling of Viscoelastic Composite Materials)
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