Effective Properties

Noels, Ludovic; Wu, Ling; Adam, Laurent; Seyfarth, Jan; Soni, Ganesh; Segurado, J.; Laschet, Gottfried; Chen, Geng; Lesueur, Maxime; Lobos, Mauricio; Böhlke, Thomas; Reiter, Thomas; Oberpeilsteiner, Stefan; Salaberger, Dietmar; Weichert, Dieter; Broeckmann, Christoph

doi:10.1002/9783527693566.ch6

Cited by 12 publications

(7 citation statements)

References 202 publications

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“…This symmetry is a consequence of the micro-scale problem resolution as shown by considering arbitrary δu ∈ U PBC in Eq. (16).…”

Section: Computational Homogenizationmentioning

confidence: 99%

“…Different multiscale techniques, see the reviews [15,16,17], have been developed analytically and/or numerically to predict the macro or mesoscopic response of heterogeneous materials at reduced computational costs while maintaining a high degree of accuracy. Among them, computational homogenization based strategies were developed in [18,19,20,21,22] and have gained popularity with the increase in computational power.…”

Section: Introductionmentioning

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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“…This symmetry is a consequence of the micro-scale problem resolution as shown by considering arbitrary δu ∈ U PBC in Eq. (16).…”

Section: Computational Homogenizationmentioning

confidence: 99%

Section: Introductionmentioning

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…The significant problem with these constitutive models consists in the prediction errors, which could arise by the fact that the real material behavior is so complex that it cannot be accurately captured by a simple model or by the difficulty in identifying the parameters. On the other hand, when considering the simulations of large-scale heterogeneous structures, multiscale models are widely developed to incorporate the information from the material microstructure and constitutive behaviors at the lower scales through a homogenization process, see reviews by [1,2]. These so-called homogenization models provide closed forms of the constitutive relationships at the structural scale while remaining of reduced computational cost as compared to the direct numerical simulations that embed the microstructural details.…”

Section: Introductionmentioning

confidence: 99%

“…A popular remedy to alleviate the computation cost in the FE 2 scheme is to substitute the microscopic BVPs by Reduced Order Models (ROM), which balance the computational cost and accuracy [5,6,7,8,9,10,11,12]. The governing equations can be solved with a reduced number of degrees of freedom in a reduced-order space based on full-field analyzes by means of proper orthogonal decomposition of the displacement field; this step is possibly followed by a so-called hyper-reduction in order to reduce the evaluation of the internal variables, see the review in [13] for a complete discussion.…”

Section: Introductionmentioning

confidence: 99%

Micromechanics-based material networks revisited from the interaction viewpoint; robust and efficient implementation for multi-phase composites

Nguyễn

Noels

2022

European Journal of Mechanics - A/Solids

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“…Homogenization-based multiscale analyses have been extensively developed; see the reviews in other works. [1][2][3] In particular, FE 2 strategies [4][5][6][7][8] have gained popularity with the increase in computational power. In such an approach, the macroscale structure defines a boundary value problem (BVP), which is solved by considering homogenized material properties extracted, at each (macro) material point of interest, from the resolution of a mesoscale BVP (see Figure 1).…”

Section: Introductionmentioning

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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Effective Properties

Cited by 12 publications

References 202 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

Micromechanics-based material networks revisited from the interaction viewpoint; robust and efficient implementation for multi-phase composites

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

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