A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials

Tran, Anh Tuan; Yvonnet, Julien; He, Qi‐Chang; Toulemonde, Charles; Sanahuja, Julien

doi:10.1016/j.cma.2011.06.012

Cited by 54 publications

(17 citation statements)

References 27 publications

(35 reference statements)

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“…Studies on wave dispersion in viscoelastic composites are relatively scarce compared with elastic problems (see Refs. for some recent investigations). Modeling research has typically focused on layered or lattice structures based on analytical and semi‐analytical approaches.…”

Section: Introductionmentioning

confidence: 94%

“…Due to the periodic assumption of microstructures in the problem domain, the elastic moduli and density depend on the microscopic coordinate vector, y, only (i.e., .x/ D .y/ and C .x; s/ D C.y; s/). Substituting Equations (16) and (20) to Equation (10) and collecting the terms of equal orders yield the equilibrium equations at each order of…”

Section: Mathematical Homogenizationmentioning

confidence: 99%

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Laplace‐domain, high‐order homogenization for transient dynamic response of viscoelastic composites

Tong

Oskay

2015

Numerical Meth Engineering

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Summary This paper presents a high‐order homogenization model for wave propagation in viscoelastic composite structures. Asymptotic expansions with multiple spatial scales are employed to formulate the homogenization model. The proposed multiscale model operates in the Laplace domain allowing the representation of linear viscoelastic constitutive relationship using a proportionality law. The high‐order terms in the asymptotic expansion of response fields are included to reproduce micro‐heterogeneity‐induced wave dispersion and formation of bandgaps. The first and second‐order influence functions and the macroscopic deformation are evaluated using the finite element method with complex coefficients in the Laplace domain. The performance of the proposed model is assessed by investigating wave propagation characteristics in layered and particulate composites and verified against direct numerical simulations and analytical solutions. The analysis of dissipated energy revealed that material dispersion may contribute significantly to wave attenuation in dissipative composite materials. The wave dispersion characteristics are shown to be sensitive to microstructure morphology. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 94%

Section: Mathematical Homogenizationmentioning

confidence: 99%

Laplace‐domain, high‐order homogenization for transient dynamic response of viscoelastic composites

Tong

Oskay

2015

Numerical Meth Engineering

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“…Constructing effective constitutive laws without prior knowledge on their form is, however, possible, but in some restricted cases. A second class of techniques is based on the construction of a numerical, material map between effective stress and strains (Terada and Kikuchi, 1995;Takano et al, 1996;Temizer and Wriggers, 2007;Yvonnet et al, 2009Yvonnet et al, , 2013Clément et al, 2012;Tran et al, 2011), which can be applied, for example, in the case of hyperelastic materials or for linear viscoelasticity, as described in the following. A third class of methodologies, valid for viscoplastic materials at small strains, uses preliminary computations to construct a basis for anelastic modes (TFA and NTFA techniques).…”

Section: Decoupled Computational Homogenization Methodsmentioning

confidence: 99%

“…In the general case, that is, for arbitrary RVE morphology and different local viscoelastic models, the form of the effective fourth-order relaxation tensor, 4 ℾ M , is unknown. However, a numerical approximation of 4 ℾ M (t) can be constructed, as proposed by Tran et al (2011). For this purpose, the numerically explicit mapping […”

Section: Decoupled Approach For Homogenization Of Linear Viscoelasticmentioning

confidence: 99%

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Geers

Kouznetsova

Matouš

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

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“…[5] and [376][377][378], employing a database to directly map the effective behavior from macroscopic information addressed in Refs. [379][380][381][382][383], transformation field analysis [384][385][386][387][388][389][390], or proper orthogonal/generalized decomposition [391-397].…”

Section: Analysis At the Rve Levelmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials

Cited by 54 publications

References 27 publications

Laplace‐domain, high‐order homogenization for transient dynamic response of viscoelastic composites

Laplace‐domain, high‐order homogenization for transient dynamic response of viscoelastic composites

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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