On mean field homogenization schemes for short fiber reinforced composites: Unified formulation, application and benchmark

Hessman, Patrick Arthur; Welschinger, Fabian; Hornberger, Kurt; Böhlke, Thomas

doi:10.1016/j.ijsolstr.2021.111141

Cited by 23 publications

(52 citation statements)

References 60 publications

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“…4 for a commercial PA6GF35, studying the necessary resolution, RVE (representative volume element) size and the influence of the mean as well as standard deviation of the length distribution on the effective elastic moduli. Moreover, we validate the approach with published experimental data [40]. The appendices provide details for determining the Weibull parameters and shed light on the similarities and differences of the exact and the maximumentropy closure.…”

Section: Contributionsmentioning

confidence: 70%

“…as determined by Hessman et al [40] with a μCT-based algorithm which identifies individual fibers [35]. Fig.…”

Section: Results Of Varying Fiber-length Parametersmentioning

confidence: 99%

“…For the work at hand, we assume that the fiber orientation and the fiber-length distribution are independent. Recent experimental data [40] suggests that there is a coupling between fiber length and fiber orientation, yet only weakly so. In particular, our working assumption may be a good starting point, in particular in view of the data available.…”

Section: Contributionsmentioning

confidence: 99%

“…The Weibull probability distribution [41] has been used frequently to model the fiber-length distribution in short-fiber composites [40,42,43]. Its density function [59, eq.…”

Section: The Weibull Distributionmentioning

confidence: 99%

“…The data is summarized in Table 2. The matrix and fiber are furnished with the isotropic elastic parameters given in Table 1 , following Hessman et al [40].…”

Section: Setupmentioning

confidence: 99%

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A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

Mehta

Schneider

2022

Comput Mech

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We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes. The algorithm permits to prescribe both a length distribution and a fiber-orientation tensor of second order, and composites with industrial filler fraction can be generated. Typically, for short-fiber composites, data on the fiber-length distribution and on the volume-weighted fiber-orientation tensor of second order is available. We consider a model where the fiber orientation and the fiber length distributions are independent, i.e., uncoupled. We discuss the use of closure approximations for this case and report on identifying the describing parameters of the frequently used Weibull distribution for modeling the fiber-length distribution. We discuss how to integrate these procedures in the Sequential Addition and Migration algorithm, developed for fibers of equal length, and work out algorithmic modifications accounting for possibly rather long fibers. We investigate the capabilities of the introduced methodology for industrial short-fiber composites, demonstrating the rather low dispersion of the effective elastic moduli for the generated unit cells.

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Section: Contributionsmentioning

confidence: 70%

“…as determined by Hessman et al [40] with a μCT-based algorithm which identifies individual fibers [35]. Fig.…”

Section: Results Of Varying Fiber-length Parametersmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

“…The Weibull probability distribution [41] has been used frequently to model the fiber-length distribution in short-fiber composites [40,42,43]. Its density function [59, eq.…”

Section: The Weibull Distributionmentioning

confidence: 99%

“…The data is summarized in Table 2. The matrix and fiber are furnished with the isotropic elastic parameters given in Table 1 , following Hessman et al [40].…”

Section: Setupmentioning

confidence: 99%

See 3 more Smart Citations

A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

Mehta

Schneider

2022

Comput Mech

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A micromechanics‐based recurrent neural networks model for path‐dependent cyclic deformation of short fiber composites

Friemann

Dashtbozorg

Fagerström

et al. 2023

Numerical Meth Engineering

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The macroscopic response of short fiber reinforced composites (SFRCs) is dependent on an extensive range of microstructural parameters. Thus, micromechanical modeling of these materials is challenging and in some cases, computationally expensive. This is particularly important when path-dependent plastic behavior is needed to be predicted. A solution to this challenge is to enhance micromechanical solutions with machine learning techniques such as artificial neural networks. In this work, a recurrent deep neural network model is trained to predict the path-dependent elasto-plastic stress response of SFRCs, given the microstructural parameters and the strain path. Micromechanical mean-field simulations are conducted to create a database for training the validating the model. The model gives very accurate predictions in a computationally efficient manner when compared with independent micromechanical simulations.

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A dual‐scale homogenization method to study the properties of chopped carbon fiber reinforced epoxy resin matrix composites

Zheng

Qiu

et al. 2022

Polymer Composites

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In this work, a dual‐scale homogenization (DSH) procedures including the representative volume element (RVE) and Unit cell (UC) with Halpin–Tsai models in the UC scale and space direction‐sensitive Hotelling expansion (SDSHE) models in RVE scale separately. These two methods are introduced and implemented to predict the response of effective elastic properties in chopped fiber reinforced epoxy matrix structures. A post‐processing scheme of subdomain in UC scale based on Gauss theorem is proposed in SDSHE method, which is used to extract the average strain and stress in UC three‐dimensional structure. In addition, the X‐ray computed tomography was used to determine the fourth order tensor orientation angle and the probability distribution information of chopped fiber length in testing samples. Homogenization properties in RVE scale, and inclusion volume fraction (VF), thickness of interface and orientation tensors are designed in UC scale and compared. The excellent correlations with experiments prove the effectiveness of the proposed models. Furthermore, the algorithm proposed in this paper realizes the homogenization of the two scales in the process of numerical analysis, and it will effectively take into account many problems that cannot be achieved by other algorithms, such as the path strain of the model, the thickness of the interface, and so on.

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On mean field homogenization schemes for short fiber reinforced composites: Unified formulation, application and benchmark

Cited by 23 publications

References 60 publications

A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

A micromechanics‐based recurrent neural networks model for path‐dependent cyclic deformation of short fiber composites

A dual‐scale homogenization method to study the properties of chopped carbon fiber reinforced epoxy resin matrix composites

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