A method of two-scale thermo-mechanical analysis for porous solids with micro-scale heat transfer

Terada, Kenjiro; Kurumatani, Mao; Ushida, T.; Kikuchi, Noboru

doi:10.1007/s00466-009-0400-9

Cited by 60 publications

(44 citation statements)

References 21 publications

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“…In the classical linearized framework for single-and multiphysics settings, this result is automatically induced through an explicit expansion of the balance laws (Pavliotis & Stuart, 2008;Sanchez-Palencia, 1980;Terada et al, 2010;Yu & Fish, 2002). Making use of these expansions together with the cell average…”

Section: Asymptotic Expansionmentioning

confidence: 99%

“…As the final branch, the first treatment of the coupled transient thermoelasticity problem in a linearized setting was presented in Francfort (1983). The coupled quasistatic problem was further investigated by Alzina, Toussaint, and Béakou (2007) while the transient case with viscous dissipation effects was considered in Francfort (1986) and Yu and Fish (2002) and recently with fluid-filled porous materials in Terada, Kurumatani, Ushida, and Kikuchi (2010). To the best knowledge of the author, an AE approach for the coupled thermoelasticity problem with finite deformation kinematics, nonlinear thermal conduction and large deviations from the equilibrium temperature has not been presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

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On the asymptotic expansion treatment of two-scale finite thermoelasticity

Temizer

2012

International Journal of Engineering Science

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a b s t r a c tThe asymptotic expansion treatment of the homogenization problem for nonlinear purely mechanical or thermal problems exists, together with the treatment of the coupled problem in the linearized setting. In this contribution, an asymptotic expansion approach to homogenization in finite thermoelasticity is presented. The treatment naturally enforces a separation of scales, thereby inducing a first-order homogenization framework that is suitable for computational implementation. Within this framework two microscopically uncoupled cell problems, where a purely mechanical one is followed by a purely thermal one, are obtained. The results are in agreement with a recently proposed approach based on the explicit enforcement of the macroscopic temperature, thereby ensuring thermodynamic consistency across the scales. Numerical investigations additionally demonstrate the computational efficiency of the two-phase homogenization framework in characterizing deformation-induced thermal anisotropy as well as its theoretical advantages in avoiding spurious size effects.

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Section: Asymptotic Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the asymptotic expansion treatment of two-scale finite thermoelasticity

Temizer

2012

International Journal of Engineering Science

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“…[398][399][400][401][402][403][404][405] for thermomechanical problems, Refs. [406][407][408][409] for magnetomechanical problems, Refs.…”

Section: Beyond Purely Elastic Problemsmentioning

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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“…In the last years, multiphysics problems have been addressed using multiscale homogenization methods, such as [96,125,120,8] for thermomechanical problems, [50,11] for magnetomechanical problems, [104,57,79] for electromechanical problems, among others. On the other hand, after the groundbreaking contribution of Bendsoe and Kikuchi [6] in which the homogenization method is used to design optimal topology structures several authors have dabbled into this actual research topic [1,106,128,56,22].…”

Section: Review Of Multiscale Methodsmentioning

confidence: 99%

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Otero

Oller

Martı́nez

2016

Arch Computat Methods Eng

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Archives of computational methods in engineering. Abstract The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical Boundary Value Problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. firstorder and second-order, in this work an enhanced-firstorder computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macroscale BVP.

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A method of two-scale thermo-mechanical analysis for porous solids with micro-scale heat transfer

Cited by 60 publications

References 21 publications

On the asymptotic expansion treatment of two-scale finite thermoelasticity

On the asymptotic expansion treatment of two-scale finite thermoelasticity

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

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

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