Toward realization of computational homogenization in practice

Yuan, Zheng; Fish, Jacob

doi:10.1002/nme.2074

Cited by 227 publications

(121 citation statements)

References 25 publications

(40 reference statements)

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“…Another reason is that for existing PBC techniques either identical meshes at opposite faces are needed with a single part mesh [1,19], either non-identical meshes at opposite faces can be handled but a unique part mesh is needed or unique material is needed. This uniqueness of the parts mesh or material is the drawback of the methods defined in [20,21]. For example, if one tries to find papers concerning the unit cell modelling of spread tow composites in the ISI web of knowledge database, one will see that no reference can be found yet.…”

Section: Introductionmentioning

confidence: 99%

Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites

Jacques

Baere

Paepegem

2014

Composites Science and Technology

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Textile fabric reinforced composites are increasingly used in structural applications in the aerospace, automotive and recreational industry. Since experimental testing is labour intensive and time consuming, numerical analysis using Representative Unit Cell (RUC) and Finite Element (FE) analyses for obtaining the elastic material constants have proven to be suitable. One of the drawbacks of the existing techniques is that one is obliged to have identical meshes on opposite faces for applying periodic boundary conditions (PBC), or that multiple part finite element meshes are not allowed. The new ORAS software discussed in this paper allows non-identical meshes at opposite faces and multiple part meshes. If a search is done in the ISI web of knowledge, no papers can be found of the meso-scale finite element modelling with periodic boundary conditions of spread tow fabric composites. With the existing techniques available on the market it is not possible, and therefore the method presented in this paper gives a solution. For the numerical meso-scale FE analysis in combination with macro homogenization for obtaining the macro elastic constants, a thermoplastic carbon-PPS (PolyPhenylene Sulfide) 5-harness satin weave composite (CETEX ® ) was used as an example. The results of the meso-scale FE analysis of the RUC using PBC with macro homogenization obtained with the new technique are in good agreement with those obtained using conventional techniques and experimental data.

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Section: Introductionmentioning

confidence: 99%

Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites

Jacques

Baere

Paepegem

2014

Composites Science and Technology

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“…While computational algorithms to implement DBC and PBC are well established and discussed by many authors [241,246,462,464,465], special care should be taken to deal with the stiffness matrix singularity due to prescribing a pure Neumann boundary condition on the RVE to implement TBC. Several authors have treated this problem using either mass-type diagonal perturbation to regularize the stiffness matrix [462], construction of a free-flexibility matrix to preserve the rigid body modes [466], adding very soft materials to the microstructure, or in the most extreme case, completely fixing enough degrees-of-freedom to make the problem well defined.…”

Section: Microdeformation Implementationmentioning

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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“…Nevertheless, in order to apply periodic boundary conditions on arbitrary finite element mesh discretization, several strategies have been proposed (e.g. [32][33][34]). …”

Section: Periodic Boundary Conditionmentioning

confidence: 99%

Determination of the size of the Representative Volume Element (RVE) for the simulation of heterogeneous polymers at finite strains

Mirkhalaf

Pires

Simões

2016

Finite Elements in Analysis and Design

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a b s t r a c tThe definition of the size of the Representative Volume Element (RVE) is extremely important for the mechanics and physics of heterogeneous materials since it should statistically represent the microstructure of the material. In the present contribution, a methodology based on statistical analysis and numerical experiments is proposed to determine the size of the RVE for heterogeneous amorphous polymers subjected to finite deformations. The approach is applied to Rubber Toughened Polystyrene (RT-PS) composed by a two phase random micro-structure. Different micro-structural samples with two different percentages of rubbery particles, namely 10% and 15%, inside the micro-structure are studied. Periodic boundary conditions (PBC) are enforced to the RVE due to their fast convergence to the theoretical/effective solution when the RVE size increases. The Finite Element Method (FEM) is used in combination with mathematical homogenization to obtain the macro-stress. Two criteria are proposed for the RVE size determination. The proposed statistical-numerical approach is general and easy to use, when compared to the previously proposed approaches, and covers other criteria available in the literature.

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Toward realization of computational homogenization in practice

Cited by 227 publications

References 25 publications

Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites

Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites

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

Determination of the size of the Representative Volume Element (RVE) for the simulation of heterogeneous polymers at finite strains

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