Homogenization method for heterogeneous material based on boundary element method

Okada, Hiroshi; Fukui, Yasuyoshi; Kumazawa, Noriyoshi

doi:10.1016/s0045-7949(01)00121-3

Cited by 24 publications

(13 citation statements)

References 27 publications

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“…Ω e(u ex ) : a : e(u ex )dΩ (18) Concerning the material properties, the Poisson ratio is set to 0.25 for the inclusion and to 0.3 for the matrix. The Young modulus ratio between the inclusion and matrix is set to 10.…”

Section: Convergence Testsmentioning

confidence: 99%

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A computational approach to handle complex microstructure geometries

Moës

Cloirec

Cartraud

et al. 2003

Computer Methods in Applied Mechanics and Engineering

583

459

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International audienceIn multiscale analysis of components, there is usually a need to solve microstructures with complex geometries. In this paper, we use the extended finite element method (X-FEM) to solve scales involving complex geometries. The X-FEM allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach. For material interfaces, this is achieved by introducing a new enrichment strategy. Although the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces. A simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement. Numerical experiments on the periodic homogenization of two-phase complex cells demonstrate the accuracy and simplicity of the X-FEM

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Section: Convergence Testsmentioning

confidence: 99%

“…The majority of studies have been based on the Finite Element Method (FEM), see [8], [12] and references herein, and only few papers present a Boundary Element Method implementation, see e.g. [10], [18]. Let us also mention the Fast Fourier Transforms based numerical method [17].…”

Section: Introductionmentioning

confidence: 99%

A computational approach to handle complex microstructure geometries

Moës

Cloirec

Cartraud

et al. 2003

Computer Methods in Applied Mechanics and Engineering

583

459

View full text Add to dashboard Cite

show abstract

“…[345][346][347] among others, in particular for granular media. Another approach to solve the boundary value problem at the microscale is the boundary element method, studied, for instance, by Kaminski [348], Okada et al [349], and Prochazka [350].…”

Section: Analysis At the Rve Levelmentioning

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 effects of reinforcement debonding on the behaviors of composites under different loading conditions are the focus of investigations by Asakawa et al (1994), Tohgo and Weng (1994) and Cho (1997). Other different methods including the homogenization method are used to evaluate the behaviors of these composites (Pierard et al, 2007;Bohm et al, 2002;Okada et al, 2001;Terada and Kikuchi, 1996). Also, Zhao and Weng (1997) studied the effective transversely isotropic moduli of two hybrid composites containing both partially debonded and perfectly bonded spheroidal inclusions.…”

Section: Introductionmentioning

confidence: 99%

Development of constitutive laws for thermomechanical behaviors of composites containing multi-type ellipsoidal reinforcements

Shabana

2009

International Journal of Solids and Structures

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a b s t r a c tComposite materials are widely used in industrial applications because of their excellent properties and behaviors. While a composite material is defined as a mixture of two or more different materials, many research works in the literature dealt with composites of only two constituents, which are matrix and one type of particles. On the other hand, the theoretical research works that dealt with more than two constituents are rare. Using some additives affects the sintering behavior, the tribological behavior and the fracture mechanics behavior of composites. For example, a suitable amount of additives as sintering aids, in the sintering process, could lower the sintering temperature, enhance phase wettability and bonding strength and improve the interlaminar fracture resistance of a composite. Therefore, it is worthwhile to develop the constitutive laws that describe the behavior of such composite materials. Accordingly, the aim of this paper is to modify the previous paper, Shabana (2003) [Shabana, Y.M., 2003. Incremental constitutive equation for discontinuously reinforced composites considering reinforcement damage and thermoelastoplasticity. Computational Materials Science 28, 31-40], in order to propose constitutive laws that predict the thermomechanical behavior of composites containing multi-type ellipsoidal reinforcements. This includes reinforcements with different materials and/or different shapes that are represented by aspect ratios. These constitutive laws not only predict the macroscopic and microscopic thermoelastoplastic behaviors of composites containing multi-type ellipsoidal reinforcements, but also characterize their different overall effective properties such as modulus of elasticity, Poison's ratio and thermal expansion coefficient in different directions. Beside this, they are applicable for porous materials and composites with multiple reinforcements and porosities of different shapes and distributions. In the present numerical analyses, composites with two, three and four constituents considering different materials and aspect ratios as well as reinforcement damage are discussed.

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Homogenization method for heterogeneous material based on boundary element method

Cited by 24 publications

References 27 publications

A computational approach to handle complex microstructure geometries

A computational approach to handle complex microstructure geometries

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

Development of constitutive laws for thermomechanical behaviors of composites containing multi-type ellipsoidal reinforcements

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