Toward stochastic multiscale methods in continuum solid mechanics

Noels, Ludovic

doi:10.1016/bs.aams.2022.03.001

Cited by 3 publications

(3 citation statements)

References 313 publications

(560 reference statements)

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“…The major challenge with sampling-based methods is the computational cost. With significant improvement of computing power, stochastic computational homogenization appears to be an emerging topic of greater interest [1,2,3,4,5]. Significant research effort has been reported on stochastic analyses of composite structures [6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

A comparative study on stochastic multiscale analysis of composite laminates

Bhattacharyya

2023

Preprint

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The progressive damage analysis of fiber composites is performed using deterministic field variables precluding the consideration of natural variability in material manufacturing. Even with high quality control techniques employed by manufacturers, there are sources of variability in the material at different spatial scales. The natural variability at microscale within the material is modeled using (1) random field approach, (2) incorporating spatially varying micro-defects. In both the approach same sampling-based non-intrusive method was adopted to incorporate aleatory uncertainty in a concurrent multiscale modeling framework. A comparison between the approaches to predict ultimate strength and stiffness of laminates is presented. Both unnotched and open-hole quasi-isotropic laminates were analyzed for validation.

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Section: Introductionmentioning

confidence: 99%

A comparative study on stochastic multiscale analysis of composite laminates

Bhattacharyya

2023

Preprint

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“…This has been done for multiple microstructures as shown in the review by L. Noels. 4 Some examples are the works on Unidirectional (UD) fiber reinforced composites, [5][6][7] on woven composites [8][9][10] and on particle-reinforced composites. 11 In most cases, a homogenization step is needed, as the macro and the microscale sizes are separated by several orders of magnitude.…”

Section: Introductionmentioning

confidence: 99%

“…In order to avoid this costly step, these random fields can be defined from micromechanical information, 2 3 that contains the statistic properties of the uncertainties present on the microstructure of the material, being then possible to generate realistic virtual microstructures that contain the same stochastic properties as the real material. This has been done for multiple microstructures as shown in the review by L. Noels 4 . Some examples are the works on Unidirectional (UD) fiber reinforced composites, 5‐7 on woven composites 8‐10 and on particle‐reinforced composites 11 .…”

Section: Introductionmentioning

confidence: 99%

A micromechanical mean‐field homogenization surrogate for the stochastic multiscale analysis of composite materials failure

Calleja Vázquez,

Wu,

Nguyen

et al. 2023

Numerical Meth Engineering

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SummaryThis paper presents the construction of a mean‐field homogenization (MFH) surrogate for nonlinear stochastic multiscale analyses of two‐phase composites that allows the material response to be studied up to its failure. The homogenized stochastic behavior of the studied unidirectional composite material is first characterized through full‐field simulations on stochastic volume elements (SVEs) of the material microstructure, permitting to capture the effect of the microstructural geometric uncertainties on the material response. Then, in order to conduct the stochastic nonlinear multiscale simulations, the microscale problem is substituted by a pressure‐dependent MFH reduced order micromechanical model, that is, a MF‐ROM, whose properties are identified by an inverse process from the full‐field SVE realizations. Homogenized stress‐strain curves can be used for the identification process of the nonlinear range, however, a loss of size objectivity is encountered once the strain softening onset is reached. This work addresses this problematic introducing a calibration of the energy release rate obtained with a nonlocal MFH micromechanical model, allowing to scale the variability found on each SVE failure characteristics to the macroscale. The obtained random effective properties are then used as input of a data‐driven stochastic model to generate the complete random fields used to feed the stochastic MF‐ROM. To show the consistency of the methodology, two MF‐ROM constructed from SVEs of two different sizes are successively considered. The performance of the MF‐ROM is then verified against an experimental transverse‐compression test and against full‐field simulations through nonlocal Stochastic Finite Element Method (SFEM) simulations. The implementation of the energy release rate calibration allows to conduct stochastic studies on the failure characteristics of material samples without the need for costly experimental campaigns, paving the way for more complete and affordable virtual testing.

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Efficient uncertainty propagation for stochastic multiscale linear elasticity

Zheng,

Nackenhorst

2024

Computer Methods in Applied Mechanics and Engineering

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Toward stochastic multiscale methods in continuum solid mechanics

Cited by 3 publications

References 313 publications

A comparative study on stochastic multiscale analysis of composite laminates

A comparative study on stochastic multiscale analysis of composite laminates

A micromechanical mean‐field homogenization surrogate for the stochastic multiscale analysis of composite materials failure

Efficient uncertainty propagation for stochastic multiscale linear elasticity

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