On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method

Banerjee, B.; Adams, Daniel O.

doi:10.1016/j.ijsolstr.2003.09.016

Cited by 43 publications

(30 citation statements)

References 26 publications

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“…With these effective properties, the analyst can replace the original heterogeneous structure with a homogeneous one and carry out structural analysis for global behavior. In the past several decades, numerous micromechanical approaches have been suggested in the literature, such as the self-consistent model (Hill, 1965;Dvorak and BaheiEl-Din, 1979;Accorsi and Nemat-Nasser, 1986), the variational approach (Hashin and Shtrikman, 1962;Milton, 2001), the method of cells (Aboudi, 1982(Aboudi, , 1989Paley and Aboudi, 1992;Williams, 2005), recursive cell method (Banerjee and Adams, 2004), mathematical homogenization theories (Bensoussan et al, 1978;Sanchez-Palencia, 1980;Murakami and Toledano, 1990), finite element approaches using conventional stress analysis of a representative volume element (Sun and Vaidya, 1996), variational asymptotic method for unit cell homogenization (VAMUCH) (Yu, 2005;Yu and Tang, 2007), and many others (see, e.g. Hollister and Kikuchi (1992), Kalamkarov et al (2009), Kanouté et al (2009) for a review).…”

Section: Introductionmentioning

confidence: 99%

Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Lee

2011

International Journal of Solids and Structures

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a b s t r a c tThe variational asymptotic method is used to construct a new model for composite plates which could have in-plane heterogeneity due to both geometry and material. We first formulate the original threedimensional problem in an intrinsic form which is suitable for geometrically nonlinear analysis. Taking advantage of smallness of the plate thickness and heterogeneity, we use the variational asymptotic method to rigorously construct an effective plate model unifying a homogenization process and a dimensional reduction process. This approach is implemented in the computer code VAPAS using the finite element technique for the purpose of dealing with realistic heterogeneous plates. A few examples are used to demonstrate the capability of this new model.

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Section: Introductionmentioning

confidence: 99%

Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Lee

2011

International Journal of Solids and Structures

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“…Researchers have proposed various techniques to either reduce the difference between the upper and lower bounds, or find an approximate value between the upper and lower bounds. Typical approaches are the self-consistent model (Hill, 1965) and its generalizations (Dvorak and Bahei-El-Din, 1979;Accorsi and Nemat-Nasser, 1986), the variational approach of Hashin and Shtrikman (1962), third-order bounds (Milton, 1981), the method of cells (MOC) (Aboudi, 1982(Aboudi, , 1989 and its variants (Paley and Aboudi, 1992;Aboudi et al, 2001;Williams, 2005b), recursive cell method (Banerjee and Adams, 2004), mathematical homogenization theories (MHT) (Bensoussan et al, 1978;Murakami and Toledano, 1990), finite element approaches using conventional stress analysis of a representative volume element (RVE) (Sun and Vaidya, 1996), and many others. Hollister and Kikuchi (1992) compared different approaches and concluded that MHT is preferable over other approaches for periodic composites even when the material is only locally periodic with a finite periodicity.…”

Section: Introductionmentioning

confidence: 99%

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Tang

2007

International Journal of Solids and Structures

174

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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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“…With these effective properties, the analyst can replace the original heterogeneous structure with a homogeneous one and carry out structural analysis for global behavior. Referring to the existing literature, numerous approaches have been suggested, such as the self-consistent model [3,11,13], the variational approach [12,24], the method of cells [1,2,26,32], recursive cell method [5], mathematical homogenization theories [6,25,28], finite element approaches using conventional stress analysis of a representative volume element [30], variational asymptotic method for unit cell homogenization (VAMUCH) [34,36], and many others. See [15,16,19] for a review.…”

Section: Introductionmentioning

confidence: 99%

Refined modeling of composite plates with in‐plane heterogeneity

Lee¹,

Yu²,

Hodges³

2013

Z Angew Math Mech

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This article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in-plane directions. By using the concept of decomposition of the rotation tensor, we first formulate the three-dimensional elastic problem in an intrinsic form for application to the geometrically nonlinear problem. The variational asymptotic method is then exercised, leading to simultaneous homogenization and dimensional reduction to construct an effective and simple model suitable for plates with in-plane periodicity. In particular, having obtained the refinement terms up to the second order, we develop a refined plate model, namely a generalized Reissner-Mindlin model that is capable of capturing the transverse shear deformations. In order to deal with realistic and complex plate geometries and constituent materials efficiently and conveniently, the proposed model is implemented into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for a few examples are compared to similar results available in the literature to demonstrate the application and performance of the present model.

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On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method

Cited by 43 publications

References 26 publications

Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

Refined modeling of composite plates with in‐plane heterogeneity

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