Multi-scale modeling of heterogeneous adhesives: Effect of particle decohesion

Kulkarni, Makarand S.; Geubelle, Philippe H.; Matouš, Karel

doi:10.1016/j.mechmat.2008.10.012

Cited by 60 publications

(54 citation statements)

References 26 publications

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“…The effect of the particle size and its distribution, volume fraction, and particle-matrix interface adhesion strength on the macroscopic failure response of heterogeneous adhesives made of stiff particles has been examined by Kulkarni et al [325] based on a multiscale cohesive framework described in Ref. [326], see also Ref.…”

Section: 22mentioning

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

178

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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Section: 22mentioning

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

178

138

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“…For a complete analysis on the sample size dependency of the homogenized stress-strain diagrams for quasi-brittle materials with a random microstructure, see [11]. On the contrary, for interface homogenization [15,14] 5 , the linear response is inversely proportional to the width of the sample i.e., being E/w for one dimensional problems. Obviously, both bulk and interface homogenizations based on standard averaging theorems give results which are not objective to the micro sample size.…”

Section: Standard Averaging Techniquesmentioning

confidence: 99%

“…In the spirit of the latter, there is a direct coupling between macro model and micro models. Figure (21) gives an schematic representation of existing computational homogenization methods for bulk material [6,7,5,8], material layers (or interfaces) [13,15,14,12] and cohesive cracks [17]. This section presents computational homogenization schemes for both cohesive and adhesive cracks using the homogenization relations developed in Section 4.…”

Section: Bulk Homogenizationmentioning

confidence: 99%

“…In the past two years homogenization schemes for adhesive cracks (or material layers) [12,13,14,15] and cohesive cracks [16,17] have been developed in which a traction-separation law is obtained based upon finite element computations at the microscale wherein the complex microstructure of the material have been explicitly modelled. By doing homogenization for adhesive cracks, in [14] the existence of an RVE for softening materials (under tensile and mixed-mode loading) which exhibit diffusive damage has been reported.…”

Section: Introductionmentioning

confidence: 99%

“…By doing homogenization for adhesive cracks, in [14] the existence of an RVE for softening materials (under tensile and mixed-mode loading) which exhibit diffusive damage has been reported. The same result has been recently presented in [15] for fibre-epoxy material that shows discrete cracking.…”

Section: Introductionmentioning

confidence: 99%

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Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Nguyen

Lloberas-Valls

Stroeven

et al. 2011

Computer Methods in Applied Mechanics and Engineering

133

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The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction-separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE 2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method.

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