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

Nguyễn, Vân Dung; Wu, Ling; Noels, Ludovic

doi:10.1007/s00466-016-1358-z

Cited by 25 publications

(42 citation statements)

References 69 publications

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“…The variational statement (18) of the Hill-Mandel condition was introduced in [68,69] and is practically implemented by defining specific boundary conditions on the meso-scale volume element whose constraint is to satisfy Eq. 14, as detailed in [70].…”

Section: Computational Homogenizationmentioning

confidence: 99%

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An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

Nguyễn

Adam³

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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An inverse Mean-Field Homogenization (MFH) process is developed to improve the computational efficiency of non-linear stochastic multiscale analyzes by relying on a micro-mechanics model. First full-field simulations of composite Stochastic Volume Element (SVE) realizations are performed to characterize the homogenized stochastic behavior. The uncertainties observed in the non-linear homogenized response, which result from the uncertainties of their micro-structures, are then translated to an incrementalsecant MFH formulation by defining the MFH input parameters as random effective properties. These effective input parameters, which correspond to the micro-structure geometrical information and to the material phases model parameters, are identified by conducting an inverse analysis from the full-field homogenized responses. Compared to the direct finite element analyzes on SVEs, the resulting stochastic MFH process reduces not only the computational cost, but also the order of uncertain parameters in the composite micro-structures, leading to a stochastic Mean-Field Reduced Order Model (MF-ROM). A data-driven stochastic model is then built in order to generate the random effective properties under the form of a random field used

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Section: Computational Homogenizationmentioning

confidence: 99%

“…The set of Eqs. (18,20) is completed by the PBCs (19) and the system is solved using the multiplier elimination method [70]. The fourth order macro-scale material tensor C M = ∂σ M ∂ε M can be extracted from this resolution.…”

Section: Computational Homogenizationmentioning

confidence: 99%

An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

Nguyễn

Adam³

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…In that case, the Hill-Mandel condition (4) is always verified. Indeed, this variational statement of the Hill-Mandel condition introduced in the works of Perić et al 46 and Schröder et al 47 (see also the work of Nguyen et al 45 ) shows that the admissible kinematic vector field  is defined by specific boundary conditions whose constraint is to satisfy Equation (7), in which case the the resolution of the microscale weak form (10) always ensures Equation (8), ie, the Hill-Mandel condition (4). Following the study on the effect of boundary conditions in the work of Wu et al, 25 only the periodic boundary conditions (PBCs) are considered in this work, for which the admissible kinematic vector field  is defined by…”

Section: Definition Of the Constrained Microscale Fe Problemmentioning

confidence: 88%

“…, where the microscale BVP stiffness matrix has been decomposed in terms of internal and boundary degrees of freedom. More details about the implementation can be found in the work of Nguyen et al 45…”

Section: Appendix a Tensorial Operations And Notationsmentioning

confidence: 99%

A micromechanics‐based inverse study for stochastic order reduction of elastic UD fiber reinforced composites analyses

Adam²,

Noels

2018

Numerical Meth Engineering

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This research develops a stochastic mean field homogenization process that is used as reduced order model to carry out a statistical multiscale analysis on unidirectional fiber reinforced composites. First, full-field simulations of unidirectional stochastic volume elements, whose statistical description is obtained from scanning electron microscope images, are conducted to define statistical mesoscale apparent properties. A stochastic Mori-Tanaka (M-T) mean field homogenization model is then developed through an inverse stochastic identification process performed on the apparent elastic properties obtained by full-field simulations. As a result, a random vector of the effective elastic properties of phases and microstructure information of the M-T model is inferred. In order to conduct stochastic finite element method analyses, a generator of this random vector is then constructed using the copula method, allowing predicting the statistical response of a composite ply under bending. The statistical dependence of the random vector entries is shown to be respected by the generator. Although this work is limited to the elastic response, we believe that the stochastic M-T model can be extended to nonlinear behaviors to conduct efficient stochastic multiscale simulations.

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“…The results will be compared with that reported in [63]. Then an entire generated RVE is computed under a uniaxial compression, using the finite element procedures proposed in [49,64]. Finally, a comparison is built between the model predictions and the experimental data provided in [37].…”

Section: Generation Of Targeted Morphologymentioning

confidence: 99%

Computational generation of open-foam representative volume elements with morphological control using distance fields

Kilingar

Kamel

Sonon

et al. 2019

European Journal of Mechanics - A/Solids

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This paper presents an automated approach to build computationally Representative Volume Elements (RVE) of open-foam cellular materials, enabling the study of the effects of the microstructural features on their macroscopic behavior. The approach strongly relies on the use of distance and level set functions. The methodology is based on the extraction of random tessellations from inclusion packings following predetermined statistical packing distribution criteria. With the help of simple recombination operations on the distance fields, the tessellations are made to degenerate in Laguerre tessellations. Predetermined morphological characteristics like strut cross-section variation based on commercially available materials are applied on the RVE to ensure the extraction of closely matching models using simple surface extraction tools, and a detailed morphology quantification of the resulting RVEs is provided by comparing them with experimental observations. The extracted RVE surface is then treated with smoothening criteria before obtaining a 3D tetrahedralized model. This model can then be exported for multi-scale simulations to assess the effects of microstructural features by an upscaling methodology. The approach is illustrated by the simulation of a compression test on an RVE incorporating plasticity with geometrically non-linear behavior.

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

Cited by 25 publications

References 69 publications

An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

A micromechanics‐based inverse study for stochastic order reduction of elastic UD fiber reinforced composites analyses

Computational generation of open-foam representative volume elements with morphological control using distance fields

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