Finite-volume micromechanics of periodic materials: Past, present and future

Cavalcante, Marcio A. A.; Pindera, Marek‐Jerzy; Khatam, Hamed

doi:10.1016/j.compositesb.2012.02.006

Cited by 78 publications

(34 citation statements)

References 62 publications

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“…While the graphite fibers are transversely isotropic, glass fibers are isotropic with a greater in plane elastic modulus contrast relative to the epoxy matrix than in the case of graphite fibers. by the corresponding moduli generated using the finite-volume direct averaging micromechanics (FVDAM) theory (Gattu et al, 2008;Khatam and Pindera, 2009), demonstrated to be comparable to that of the finite element method (Cavalcante et al, 2012) by Drago and Pindera (2008) for square arrays of isotropic inclusion/matrix phases, and is also the case in the present study. A demanding test of the solution's stability is the demonstration that in the limit as the fiber volume fraction becomes very small, the solution reduces to the Eshelby solution (Eshelby, 1957) with just the first few terms remaining, and the higher-order coefficients becoming vanishingly small.…”

Section: Discussionsupporting

confidence: 49%

“…At present, most homogenization techniques for periodic materials continue to rely on numerical solutions of the unit cell boundary-value problem using mainly finite-element and finite-volume techniques, and to a lesser extent techniques based on finite-difference and Fourier transform approaches (Michel et al, 1999;Pindera et al, 2009;Charalambakis, 2010;Cavalcante et al, 2012;Tu and Pindera, 2014). The finite-element technique is the dominant method mainly because of the easy-to-use character and wide availability of commercial packages.…”

Section: Ruc-based Approachesmentioning

confidence: 99%

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Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

Wang

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This dissertation describes the construction, validation and applications of a stable and quickly converging elasticity-based locally exact homogenization theory for unidirectionallyreinforced composites. Elasticity-based homogenization approaches offer a number of advantages relative to finite-element, finite-difference or finite-volume homogenization schemes, including extremely fast input data construction, ability to investigate composites with very thin coatings or interphases without experiencing convergence issues common to finite-element analyses, and ability to efficiently accommodate phases with cylindrically orthotropic constituents without much effort. The constructed homogenization theory enables efficient analysis of the elastic and viscoelastic response of unidirectional composite materials with rectangular, square, hexagonal and tetragonal periodic microstructures comprised of isotropic, transversely isotropic, and (cylindrically or circumferentially) orthotropic phase constituents, and third phases such as coatings or interphases.The success of this homogenization theory is rooted in the balanced variational principle which plays a key role in the implementation of non-separable periodic boundary conditions, leading to quickly-converging homogenized moduli and stable local stress distributions. This variational principle, originally proposed by Drago and Pindera (2008) for rectangular unit cell architectures, was extended herein to hexagonal and tetragonal unit cells and demonstrated to produce quickly converging homogenized moduli and local stress fields regardless of phase modulus contrast, orthotropy type or viscoelasticity effects.The constructed homogenization theory has been validated upon comparison with known elasticity solutions and micromechanics models. These include the solution to the Eshelby problem which was used as a benchmark to demonstrate the robustness and stability of the developed unit cell solution approach, and the finite volume direct averaging micromechanics (FVDAM) theory which produces high-fidelity results comparable to the finite-element method.Comparison with the classical composite cylinder assemblage (CCA) and Mori-Tanaka micromechanics models establishes applicability and limitations of these approaches based on simplified geometric representation of composite material microstructures. Selected numerical results are generated to provide insight into the efficiency and robustness of the theory. To demonstrate its advantage, the key component of the theory, namely the balanced variational principle, is compared with recently adopted approaches based on a derivative variational principle proposed originally in the context of locally-exact finite-element solutions. Finally, the elastic problem has been extended to viscoelastic domain via the elastic-viscoelastic correspondence principle, validated at the homogenized and local field levels at different times, and employed to investigate thus-far undocumented features of time-dependent response of polymeric ma...

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Section: Discussionsupporting

confidence: 49%

Section: Ruc-based Approachesmentioning

confidence: 99%

Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

Wang

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“…The CV method has also been applied to plate bending problems where both the cell centred [17] and vertex centred methods [18] have shown to be locking free for thick and thin Mindlin plates. In recent developments control volumes have been used in the structural analysis of radio frequency MEMS devices [19] and in the analysis of the micromechanics of periodic materials [20].…”

Section: Introductionmentioning

confidence: 99%

A higher order control volume based finite element method to predict the deformation of heterogeneous materials

Beveridge

Wheel

Nash

2013

Computers & Structures

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Materials with obvious internal structure can exhibit behaviour, under loading, that cannot be described by classical elasticity. It is therefore important to develop computational tools incorporating appropriate constitutive theories that can capture their unconventional behaviour. One such theory is micropolar elasticity. This paper presents a linear strain control volume finite element formulation incorporating micropolar elasticity. Verification results from a micropolar element patch test as well as convergence results for a stress concentration problem are included. The element will be shown to pass the patch test and also exhibit accuracy that is at least equivalent to its finite element counterpart.

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“…This version was the most updated one when the author initiated his work whilst the development of the generalized version of FVDAM was taking place in parallel. Although interfacial interpenetration and discontinuity of non-traction stress components occur in the standard parametric FVDAM theory, (Cavalcante et al 2012), the surface-averaged values of both traction and non-traction stress components are reliable, Cavalcante et al, (2008Cavalcante et al, ( , 2011, especially if the heterogeneous materials are not subjected to large deformation, Khatam and Pindera (2012), which is the scenario of interest herein.…”

Section: Methodsmentioning

confidence: 99%

“…In contrast to variational techniques, local equilibrium is satisfied in integral sense at the discretized subdomain level in the finite-volume method, offering solution stability and other advantages, Cavalcante et al (2012). There are three variants of finite-volume methods that can be identified in the analysis of solid mechanics problems: the cell-centered finite-volume technique, the cellvertex finite-volume techniques and the surface averaging finite-volume techniques.…”

Section: Finite-volume Theories In Solid Mechanics Applicationsmentioning

confidence: 99%

CZM-based Finite-Volume Homogenization and Optimization of Periodic Composites

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Finite-volume micromechanics of periodic materials: Past, present and future

Cited by 78 publications

References 62 publications

Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

A higher order control volume based finite element method to predict the deformation of heterogeneous materials

CZM-based Finite-Volume Homogenization and Optimization of Periodic Composites

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