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Computational homogenization

Computational homogenization of cellular materials

Computational homogenization of cellular materials

... second–order computational homogenization, the material length scale is directly related to the size of the RVE [49] and the localization band results from the micro–bucklings, but the behavior is ...

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Unified treatment of microscopic boundary conditions in computational homogenization method for multiphysics problems

Unified treatment of microscopic boundary conditions in computational homogenization method for multiphysics problems

... • Computational homogenization scheme for micro-structured materials – Macro-micro transition • The deformed state of the microscopic BVP is conducted by macroscopic kinematic variables • Macro-micro ...

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Computational homogenization of cellular materials with propagation of instabilities through the scales

Computational homogenization of cellular materials with propagation of instabilities through the scales

... multi–scale computational homogenization scheme looses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second–order multi–scale computational ...

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Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches

Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches

... another computational approach for incorporating images in models, based on the extended finite element method (X-FEM) and ...of computational homogenization in elasticity, starting from material ...

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Computational homogenization of cellular materials capturing micro-buckling, macro-localization and size effects

Computational homogenization of cellular materials capturing micro-buckling, macro-localization and size effects

... The computational homogenization approach is probably the most accurate tech- nique for micro–structured materials with highly non–linear behaviors and allows as- sessing the macroscopic influence of the ...

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Computational homogenization of nano-materials accounting for size effects via surface elasticity

Computational homogenization of nano-materials accounting for size effects via surface elasticity

... and homogenization. The main principles of homogenization were introduced by Hill [25] and Hill and Rice [26] as a consistent methodology to link the macroscopic and microscopic ...scales. ...

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Model reduction in computational homogenization for transient heat conduction

Model reduction in computational homogenization for transient heat conduction

... Similarly, in transient heat conduction problems, the relaxed separation of scales constitutes a thermal diffusion phenomenon in which the matrix remains in steady-state under transient thermal loads and only the ...

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Variationally consistent computational homogenization of transient heat conduction using Craig-Bampton mode synthesis

Variationally consistent computational homogenization of transient heat conduction using Craig-Bampton mode synthesis

... However, when the phenomena is highly transient, these assumptions do not hold true for homogenization pur- poses. Also, the micro-scale length scales and high contrast in material properties exhibit to transient ...

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Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

... though computational homogenization schemes are largely described in the lit- erature, the numerical treatments of the constrained micro-scale BVP and of its boundary condition are often specialized to the ...

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Computational Homogenization of Architectured Materials

Computational Homogenization of Architectured Materials

... 4.4 Statistical Representative Volume Element Size for Computational Homogenization For non-periodic architectured materials, the problem of representativity of samples can be addressed [r] ...

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Computational Homogenization of Architectured Materials

Computational Homogenization of Architectured Materials

... 4.4 Statistical Representative Volume Element Size for Computational Homogenization For non-periodic architectured materials, the problem of representativity of samples can be addressed [r] ...

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Derivation of the Young's and shear moduli of single-walled carbon nanotubes through a computational homogenization approach

Derivation of the Young's and shear moduli of single-walled carbon nanotubes through a computational homogenization approach

... It was found that the Young's modulus is noticeably dependent on the nanotube diameter, as the tube diameter is small Gupta and Batra (2008) have used molecular mechanics to study th[r] ...

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Computational homogenization of periodic beam-like structures

Computational homogenization of periodic beam-like structures

... Thus, three homogenization approaches are available, with their own domain of validity. Our objective here is not to discuss these different methods, the interested reader is referred to Buannic and Cartraud ...

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Multiscale homogenization of multilayered structures

Multiscale homogenization of multilayered structures

... with computational homogenization techniques in order to reduce the computational cost of three - dimensional ...lower computational cost, the flexibility and the great adaptativity to many ...

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The Periodic Unfolding Method in Homogenization

The Periodic Unfolding Method in Homogenization

... The same dilation operator was used by Bourgeat, Luckhaus, and Mikelic in [16] under the name of “periodic modulation.” Proposition 4.6 of [16] showed that if a sequence two-scale conver[r] ...

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Quantitative stochastic homogenization of convex integral functionals

Quantitative stochastic homogenization of convex integral functionals

... 2. Subadditive and superadditive energies The analysis in the first part of this paper is centered on two monotone quantities involving the energy. Up to normalizing factors, one is subadditive and the other is ...

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Random integrals and correctors in homogenization

Random integrals and correctors in homogenization

... the analysis of the correctors to homogenization. The convergence in distribution in the space of continuous paths of such processes to a Gaussian processes is summarized in theorem 4.1. The theoretical results ...

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Interior error estimate for periodic homogenization

Interior error estimate for periodic homogenization

... the homogenization of the classical problem of diffusion in a bounded domain with sufficiently smooth boundary we proved that the error is of order ε 1/2 ...

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Effective diffusion tensor computed by homogenization

Effective diffusion tensor computed by homogenization

... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou ...

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Effective Diffusion Tensor Computed by Homogenization

Effective Diffusion Tensor Computed by Homogenization

... by homogenization Dang Van Nguyen 1 , Denis Grebenkov 2 , Cyril Poupon 3 , Denis Le Bihan 3 , and Jing-Rebecca Li 4 1 CMAP, Ecole Polytechnique, Palaiseau Cedex, France, 2 PMC, Ecole Polytechnique, Palaiseau ...

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