A three-dimensional, higher-order, elasticity-based micromechanics model

Williams, Todd O.

doi:10.1016/j.ijsolstr.2004.06.056

Cited by 15 publications

(12 citation statements)

References 15 publications

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“…It is easy to verify that Sun and Vaidya's FEM approach is equally applicable to particle reinforced composites. Two other approaches we believe will provide critical evaluations for VAMUCH are the 3D version of ECM (Williams, 2005a) and an approach based on mathematical homogenization theory and finite element method (Banks-Sills et al, 1997) (later we follow Williams (2005a) to name this approach as HFE).…”

Section: Particle Reinforced Compositesmentioning

confidence: 99%

“…We are surprised to find out that it is counter intuitive that the predictions of 5th order ECM are worse than 3rd order ECM for this particular case. It is worthy to point out that the data of HFE and ECM are provided independently by the author of Williams (2005a), where ECM data are calculated and HFE data are directly picked out from the plots in Banks-Sills et al (1997). 2 The isotropic assumption is convenient for comparing with available results in the literature.…”

Section: Particle Reinforced Compositesmentioning

confidence: 99%

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Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Tang

2007

International Journal of Solids and Structures

169

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A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.

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Section: Particle Reinforced Compositesmentioning

confidence: 99%

Section: Particle Reinforced Compositesmentioning

confidence: 99%

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Tang

2007

International Journal of Solids and Structures

169

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“…Figures 5 (a) and (b) show the effective Young's modulus and Poisson ratio, respectively, for an increasing particle volume fraction. The reference solutions are those of a SwiftComp 3D model, ECM of 3 rd and 5 th order from Williams [24] and a mathematical homogenization approach (MHT) from Banks-Sills [25]. …”

Section: Homogenizationmentioning

confidence: 99%

Micromechanics Modeling of Unit Cells Using CUF Beam Models and the Mechanics of Structure Genome

Miguel¹,

Pagani²,

Yu³

et al. 2017

American Society for Composites 2017

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“…The Elasticity-Based Cell Model (ECM) 5,11,12 starts with the same type of microstructural discretization as used by the original GMC theory, Fig. 1.…”

Section: The Elasticity-based Cell Model (Ecm)mentioning

confidence: 99%

A Critical Evaluation of the Predictive Capabilities of Various Advanced Micromechanics Models

Williams

Bednarcyk

et al. 2007

48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The focus of this work is to critically evaluate the predictive capabilities of several advanced micromechanics models, including GMC, HFGMC, ECM, and VAMUCH. The comparison concentrates primarily on predictions for the effective elastic properties and local stress fields based on micromechanics approaches for various types of composite systems. Both exact analytical solutions and finite element simulations will be utilized in the comparison to assess the accuracy of the different models. It is found that for some microstructures, most of the compared models provide similar and reliable predictions for effective properties. For an accurate prediction for local stress distributions, HFGMC and VAMUCH significantly outperform GMC, which provides only average local fields. A very challenging X shape microstructure is also proposed in this paper which pushes all the micromechanics models to their limits. This case clearly discloses the fallacy about micromechanics that every model "works" as far as effective properties concerned. Such an assessment can help engineers choose the appropriate micromechanics model for composites they are dealing with in their applications.

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A three-dimensional, higher-order, elasticity-based micromechanics model

Cited by 15 publications

References 15 publications

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Micromechanics Modeling of Unit Cells Using CUF Beam Models and the Mechanics of Structure Genome

A Critical Evaluation of the Predictive Capabilities of Various Advanced Micromechanics Models

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