Homogenization methods for multi-phase elastic composites with non-elliptical reinforcements: Comparisons and benchmarks

Klusemann, Benjamin; Böhm, H.J.; Svendsen, Bob

doi:10.1016/j.euromechsol.2011.12.002

Cited by 100 publications

(77 citation statements)

References 68 publications

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“…The chosen linear-elastic range and a small volume fraction (concentration) of fibres allow to employ the mean-field homogenisation approach to formulate the constitutive relation for SFRC [23,79,80]. Essentially, the concrete is a heterogeneous material consisting of cement binder and aggregate of different fractions, Fig.…”

Section: Constitutive Relation For One Meso-volume Element Of Sfrcmentioning

confidence: 99%

DC-conductivity testing combined with photometry for measuring fibre orientations in SFRC

et al. 2013

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Dissertation for the Doctoral degree to be presented with due permissions of the School of Engineering, Aalto University and Tallinn University of Technology for public examination and debate in Auditorium R1 (Rakentajanaukio 4A) at the Aalto University (Espoo, Finland) on the 4th of April 2014 at 12 noon. Aalto University School of Engineering Tallinn University of TechnologyS up e r v i s i ng p r o f e s s o r P ro f e s s o r J ari P ut t o ne n, A al t o U ni v e rs i t y , F i nl and T h e s i s a d v i s o r D r. re r. nat . H e i k o H e rrmann, T al l i nn U ni v e rs i t y o f T e c h no l o g y , E s t o ni aP r e l i mi na r y e x a mi ne r s P ro f e s s o r H o l m A l t e nb ac h , F ac ul t y o f M e c h ani c al E ng i ne e ri ng , O t t ov o n G ue ri c k e -U ni v e rs i t ät M ag d e b urg , G e rmany P ro f e s s o r K e nne t h R une s s o n, D e p art me nt o f A p p l i e d M e c h ani c s , C h al me rs U ni v e rs i t y o f T e c h no l o g y , S w e d e n O p p o ne nt P ro f e s s o r K ari n L und g re n, D e p art me nt o f C i v i l and E nv i ro nme nt al E ng i ne e ri ng , C h al me rs U ni v e rs i t y o f T e c h no l o g y , S w e d e n A al t o U ni v e rs i t y p ub l i c at i o n s e ri e s D O C T O R A L D I S S E R T A T I O N S 2 8/ 2 0 1 4© M ari k a E i k I S BN 9 7 8-9 5 2 -6 0 -5 5 9 1 -6 I S BN 9 7 8-9 5 2 -6 0 -5 5 9 2 -3 ( p d f ) I S S N -L 1 7 9 9 -4 9 34 I S S N 1 7 9 9 -4 9 34 ( p ri nt e d ) I S S N 1 7 9 9 -4 9 4 2 ( p d f ) h t t p : / / urn. f i / U R N : I S BN : 9 7 8-9 5 2 -6 0 -5 5 9 2 -3 U ni g raf i a O y H e l s i nk i 2 0 1 4 F i nl and S up e r v i s i ng p r o f e s s o r P ro f e s s o r J ari P ut t o ne n, A al t o U ni v e rs i t y , F i nl andT h e s i s a d v i s o r D r. re r. nat . H e i k o H e rrmann, T al l i nn U ni v e rs i t y o f T e c h no l o g y , E s t o ni a P r e l i mi na r y e x a mi ne r s P ro f e s s o r H o l m A l t e nb ac h , F ac ul t y o f M e c h ani c al E ng i ne e ri ng , O t t ov o n G ue ri c k e -U ni v e rs i t ät M ag d e b urg , G e rmany P ro f e s s o r K e nne t h R une s s o n, D e p art me nt o f A p p l i e d M e c h ani c s , C h al me rs U ni v e rs i t y o f T e c h no l o g y , S w e d e n O p p o ne nt P ro f e s s o r K ari n L und g re n, D e p art me nt o f C i v i l and E nv i ro nme nt al E ng i ne e ri ng , C h al me rs U ni v e rs i t y o f T e c h no l o g y , S w e d e n A al t o U ni v e rs i t y p ub l i c at i o n s e ri e s D O C T O R A L D I S S E R T A T I O N S 2 8/ 2 0 1 4 © M ari k a E i k I S BN 9 7 8-9 5 2 -6 0 -5 5 9 1 -6 I S BN 9 7 8-9 5 2 -6 0 -5 5 9 2 -3 ( p d f ) I S S N -L 1 7 9 9 -4 9 34 I S S N 1 7 9 9 -4 9 34 ( p ri nt e d ) I S S N 1 7 9 9 -4 9 4 2 ( p d f ) h t t p : / / urn. f i / U R N : I S BN : 9 7 8-9 5 2 -6 0 -5 5 9 2 -3 U ni g raf i a O y H e l s i nk i 2 0 1 4 F i nl and S up e r v i s i ng p r o f e s s o r P ro f e s s o r J ari P ut t o ne n, A al t o U ni v e rs i t y , F i nl and © M ari k a E i k I S BN 9 7 8-9 5 2 -6 0 -5 5 9 1 -6 I S BN 9 7 8-...

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Section: Constitutive Relation For One Meso-volume Element Of Sfrcmentioning

confidence: 99%

DC-conductivity testing combined with photometry for measuring fibre orientations in SFRC

et al. 2013

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“…Detailed reviews and comparisons of analytical models of micromechanics can be found in Ref. [177][178][179][180][181][182][183][184][185][186][187][188][189][190][191][192][193][194][195][196]. In particular, see the review by Mura et al [182].…”

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

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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“…The irreducible decomposition of the Eshelby's tensor by Zou et al (2010) and Klusemann et al (2012) is combined with a rectangular aspect ratio to provide the Graphene sheet with an averaged Eshelby's tensor for homogenisation purposes.…”

Section: Introductionmentioning

confidence: 99%

“…They formulate some remarks about the elliptical approximation to the average of ETF which is valid for a convex non-elliptical inclusion but becomes unacceptable for a non-convex non-elliptical inclusion. Based on the results of Zou et al (2010) mainly the averaged Eshelby's tensor, Klusemann et al (2012) has investigated the effective responses of composites consisting of non-elliptical shape in the context of several homogenisation methods.…”

Section: Introductionmentioning

confidence: 99%

Non-linear elastic moduli of Graphene sheet-reinforced polymer composites

Elmarakbi

Wang

Azoti

2016

International Journal of Solids and Structures

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The non-linear elastic moduli of the Graphene sheet-reinforced polymer composite are investigated using a combined molecular mechanics theory and continuum homogenisation tools. Under uniaxial loading, the linear and non-linear constitutive equations of the Graphene sheet are derived from a Taylor series expansion in powers of strains. Based on the modified Morse potential, the elastic moduli and Poisson's ratio are obtained for the Graphene sheet leading to the derivation of the non-linear stiffness tensor. For homogenisation purpose, the strain concentration tensor is computed by the means of the irreducible decomposition of the Eshelby's tensor for an arbitrary domain. Therefore, a mathematical expression of the averaged Eshelby's tensor for a rectangular shape is obtained for the Graphene sheet. Under the Mori-Tanaka micro-mechanics scheme, the effective non-linear behaviour is predicted for various micro-parameters such as the aspect ratio and mass fractions. Numerical results highlight the effect of such micro-parameters on the anisotropic degree of the composite.

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Homogenization methods for multi-phase elastic composites with non-elliptical reinforcements: Comparisons and benchmarks

Cited by 100 publications

References 68 publications

DC-conductivity testing combined with photometry for measuring fibre orientations in SFRC

DC-conductivity testing combined with photometry for measuring fibre orientations in SFRC

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

Non-linear elastic moduli of Graphene sheet-reinforced polymer composites

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