On the asymptotic expansion treatment of two-scale finite thermoelasticity

Temizer, İ.

doi:10.1016/j.ijengsci.2012.01.003

Cited by 43 publications

(27 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This modification reflects the macroscopic observation that as ϵ → 0, the temperature within the material in the vicinity of the contact interface remains approximately equal to

{\overset{θ}{falsemml-overline}}_{c}

. This explicit enforcement of

{\overset{θ}{falsemml-overline}}_{c}

, similar to the ideas in , decouples the micromechanical analysis into two phases: Mechanical phase : The macroscopic contact pressure is applied to the two samples within a purely mechanical contact problem to solve for the deformed configuration and thereby resolve the real contact area. Within this setup, all temperature‐dependent material properties are evaluated at

{\overset{θ}{falsemml-overline}}_{c}

. Thermal phase : On the frozen mechanical configuration with a resolved contact interface, a purely thermal problem is solved where the macroscopic normal heat flux

\overset{h}{falsemml-overline}

is enforced and the temperature jump

{\overset{ϑ}{falsemml-overline}}_{c}^{(I)}

is measured via .…”

Section: A Two‐phase Self‐consistent Frameworkmentioning

confidence: 52%

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

Temizer

2013

Int. J. Numer. Meth. Engng

View full text Add to dashboard Cite

SUMMARYA computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two-phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two-phase framework is cast within a self-consistent iterative scheme that acts as a first-order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar-based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non-uniform rational B-spline basis functions. Overall, the two-phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures.

show abstract

“…This modification reflects the macroscopic observation that as ϵ → 0, the temperature within the material in the vicinity of the contact interface remains approximately equal to

{\overset{θ}{falsemml-overline}}_{c}

. This explicit enforcement of

{\overset{θ}{falsemml-overline}}_{c}

{\overset{θ}{falsemml-overline}}_{c}

. Thermal phase : On the frozen mechanical configuration with a resolved contact interface, a purely thermal problem is solved where the macroscopic normal heat flux

\overset{h}{falsemml-overline}

is enforced and the temperature jump

{\overset{ϑ}{falsemml-overline}}_{c}^{(I)}

is measured via .…”

Section: A Two‐phase Self‐consistent Frameworkmentioning

confidence: 52%

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

Temizer

2013

Int. J. Numer. Meth. Engng

View full text Add to dashboard Cite

show abstract

“…Fish and co-workers presented a generalization of the mathematical homogenization method based on double-scale asymptotic expansion to account for non-linear effects such as plasticity [28] and damage [29] in heterogeneous media. The asymptotic homogenization method was continuously developed and nowadays, it still is a very popular research topic [12,52,15,18,119].…”

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

View full text Add to dashboard Cite

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.

show abstract

“…An extensive body of literature is devoted to study this technique among which we refer to Refs. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Reviews of the different multiscale approaches can be found in Refs.…”

Section: Introductionmentioning

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

View full text Add to dashboard Cite

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.

show abstract

On the asymptotic expansion treatment of two-scale finite thermoelasticity

Cited by 43 publications

References 21 publications

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

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

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

Contact Info

Product

Resources

About