Homogenization in finite thermoelasticity

Temizer, İ.; Wriggers, Peter

doi:10.1016/j.jmps.2010.10.004

Cited by 100 publications

(90 citation statements)

References 88 publications

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“…See also Torquato (2002) and Pavliotis and Stuart (2008) for recent overviews. The goal of this contribution is to highlight the AE basis for a homogenization framework in finite thermoelasticity that was recently proposed in Temizer and Wriggers (2011). A concise presentation is pursued with references exclusively concentrating on works where an explicit AE approach has been investigated for thermomechanical problems.…”

Section: Introductionmentioning

confidence: 99%

“…A concise presentation is pursued with references exclusively concentrating on works where an explicit AE approach has been investigated for thermomechanical problems. See Temizer and Wriggers (2011) for extensive references on closely related approaches in various multiphysics problems.…”

Section: Introductionmentioning

confidence: 99%

“…These approaches were critically examined in Temizer and Wriggers (2011) and two major shortcomings were pointed out in the literature: (i) the coupled nature of the macroscopic boundary value problem has not been investigated to full extent in a transient setting, and (ii) a separation of scales assumption has not been preserved. While the first shortcoming is important from a numerical point of view, the second one is essential in order to avoid non-physical size effects and confirm consistency with earlier single-physics approaches.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…[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%

“…In this section, fundamental definitions and concepts of the theory of computational homogenization are briefly addressed in order for this paper to be self-contained. In this contribution, all relations are represented only in Lagrangian description, considering that it is straightforward to formulate the problem in Eulerian description [206,402,408,458]. Furthermore, it is possible to establish the homogenization theory based on Green-Lagrange strain and Piola-Kirchhoff stress as alternatively suitable strain and stress measures [459,460].…”

Section: Theorymentioning

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

185

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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Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations

Eden

Muntean

2017

Math Methods in App Sciences

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We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two‐phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ϵ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ϵ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ϵ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.

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Homogenization in finite thermoelasticity

Cited by 100 publications

References 88 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

Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations

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