Using Asymptotic Homogenization in Parametric Space to Determine Effective Thermo-Viscoelastic Properties of Fibrous Composites

Vlasov, A. N.; Volkov-Bogorodsky, Dmitriy B.; Savatorova, Viktoria L.

doi:10.1007/978-3-031-22401-0_10

Cited by 2 publications

(18 citation statements)

References 23 publications

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“…Below we present the method of asymptotic homogenization in parametric space [39,40,[42][43][44] for fiberreinforced composite with an interphase layer and use it to obtain effective characteristics of a fiberreinforced composite with an intermediate layer.…”

Section: Asymptotic Homogenization In Parametric Spacementioning

confidence: 99%

“…D i 1 denotes the derivative of a function with respect to slow variable x i 1 regardless of the fast variable. Substituting the asymptotic expansions ( 8) and ( 9) into equations ( 6) and ( 7) and collecting the terms of the order of O(e À1 ), we are getting the system of equations [39,40,44]:…”

Section: Asymptotic Homogenization In Parametric Spacementioning

confidence: 99%

“…Here, we utilize an analytical-numerical approach to the solution of the cell problem, introduced in Vlasov et al [40]. For this purpose, we use the solutions of the generalized Eshelby problem [8,47] as basic functions for the Trefftz method [48].…”

Section: Analytical-numerical Approach To the Solution Of The Problem...mentioning

confidence: 99%

“…One can make use of the correspondence principle to transform time-dependent viscoelastic problems into symbolic elastic ones in the Laplace or Fourier domain. When it comes to using asymptotic homogenization to model viscoelastic materials, we would like to refer to papers [31,[35][36][37][38][39][40]. Cruz-Gonza´lez et al [31] reported analytical expressions of effective properties of one-dimensional viscoelastic composites obtained using the Laplace transform, asymptotic homogenization, and inverse Laplace transform.…”

Section: Introductionmentioning

confidence: 99%

“…These last results were obtained for the Maxwell model using finite-volume direct averaging micromechanics and finite element method. Recently, we submitted the paper [40], where the Maxwell model and the analytical-numerical method of asymptotic homogenization in parametric space were used to determine effective thermo-viscoelastic properties of materials composed of elastic fibers embedded in viscoelastic matrix (no interphase layer was discussed).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer

Vlasov

Volkov-Bogorodsky

Savatorova

2022

Mathematics and Mechanics of Solids

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In this paper, we apply the method of asymptotic homogenization in parametric space in order to determine thermo-viscoelastic properties of materials composed of cylindrical fibers surrounding by an intermediate layer separating them from viscoelastic matrix. We use the Maxwell model of viscoelasticity. The volumetric fraction and physical properties of the layer can vary. There is a possibility of a contrast between the properties of fibers, the layer, and the matrix. Our approach allows us to treat temperature as a parameter and study the response of mechanical characteristics on the change in temperature. We perform the Fourier transform of governing equations and then implement asymptotic homogenization of the resulting equations in parametric space. Microscopic boundary value problem is defined on a periodic cell consisting of a fiber surrounded by a layer and embedded in the matrix. Macroscopic equations are derived for the complex Young’s and shear moduli. Effective viscoelastic properties of the material are computed for different values of the frequency of harmonic oscillations and for various temperatures. This paper discusses how effective storage and loss Young’s and shear moduli depend on volumetric fraction and mechanical properties of the material of the layer. The obtained results can provide information on how concentration, structure and properties of inclusions can affect the effective storage and loss Young’s and shear moduli.

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Section: Asymptotic Homogenization In Parametric Spacementioning

confidence: 99%

Section: Asymptotic Homogenization In Parametric Spacementioning

confidence: 99%

Section: Analytical-numerical Approach To the Solution Of The Problem...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer

Vlasov

Volkov-Bogorodsky

Savatorova

2022

Mathematics and Mechanics of Solids

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Effective Properties of Homogenised Nonlinear Viscoelastic Composites

Roque-Piedra,

Rodríguez-Ramos,

Penta

et al. 2023

Materials

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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.

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Using Asymptotic Homogenization in Parametric Space to Determine Effective Thermo-Viscoelastic Properties of Fibrous Composites

Cited by 2 publications

References 23 publications

Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer

Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer

Effective Properties of Homogenised Nonlinear Viscoelastic Composites

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