On micro–macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials

Markovič, Damijan; Ibrahimbegović, Adnan

doi:10.1016/j.cma.2003.12.072

Cited by 62 publications

(44 citation statements)

References 25 publications

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“…In fact, is doubtful to deal with SWCNTs as a continuum body, as has been shown through the great scattering observed in the Poisson's ratio calculated by using eq. (42). Therefore, the classical constitutive relations do not suitably render a continuum equivalent medium for SWCNTs.…”

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confidence: 99%

“…7. The application of standard homogenization theories [41], [42] could be very promising to treat the mechanical simulation of CNTs (although our paper is not directly related to these methods), given the specific characteristics of the problem (great number of unit cells which are repeated with geometric periodicity). Likewise, it would be taken tensile, compressive, flexural and torsional behavior as the preferred set of simple loading test cases for establishing the equivalent properties into the homogenization solution.…”

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confidence: 99%

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A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

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ElsevierMerli Gisbert, R.; Lazaro, C.; Monleón Cremades, S.; Domingo Cabo, A. (2013). A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation. Computers and Structures. 127:68-87. doi:10.1016/j.compstruc.2012.11.023 AbstractA new general formulation for the mechanical behavior of Single-Walled Carbon Nanotubes is presented. Carbon atoms are located at the nodes of an hexagonal honeycomb lattice wrapped into a cylinder. They are linked by covalent C − C bonds represented by a truss or spring element, and the three-body interaction among two neighboring covalent bonds is reproduced by a rotational spring. The main advantage of our approach is to allow general load conditions (and any chirality) with no need of specific formulation for each load case, in contrast with previous works [26], [27], [31]. Four load configurations are adopted: tension, compression, bending and torsion of cantivelered SWCNTs. Calculations with our own codes for both AMBER and Morse potential functions have been carried out, aimed to compare their final results. Initial positions of the atoms (nodes) into nanotube cylindrical geometry has been reproduced in great detail by means of a conformal mapping from the planar graphene sheet. Therefore, the effect of initial SWCNTs curvature has been introduced explicitly through a system of initial stresses (prestressed state) which contribute to maintain their circular cross-section. Numerical results and deformed shapes for nanotubes with several diameters and chiralities under each load case are used to obtain their mechanical parameters with the only objective of checking the present formulation with previous works [28], [30], [20], [24]. Also, the significance of the atomistic discrete simulations at the nano-scale size against other continuum models is underlined.

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confidence: 99%

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confidence: 99%

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

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“…Multiscale models are traditionally categorized into the homogenization method, where the length scales of micro-and macroproblems are sufficiently separate, and the concurrent method, see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], which considers strong coupling between the scales. 2 This contribution details on the former one.…”

Section: Introductionmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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“…It is of interest to note at this stage that this methodology has some similarities with certain superposition-based multiscale methods that have been proposed long before the concept of non-intrusiveness was introduced (see, e.g, [23] for an overview). These techniques appear in the literature under different names, for example the Chimera method [24], the variational multiscale method [25,26], the FE patches method [27], the numerical zoom [28], the strong coupling method [29], and the hp-d method [30,31]. It should, nevertheless, be stressed that these techniques lead to an approximate solution that is expressed as the sum of a global solution and a local correction whereas, in the non-intrusive strategy, the global response is completely eliminated in the zone of interest, its place being taken by the local solution.…”

Section: Introductionmentioning

confidence: 99%

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

Guinard

Bouclier

Toniolli

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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The multiscale analysis of large composite aeronautical structures involves the development of robust coupling strategies. Among the latter, non-intrusive coupling is attractive, since it is able to consistently connect a global simplified linear model to a local detailed one, using features available in commercial software. Up to now, such coupling methods were still limited to academic situations where global and local meshes are geometrically and/or topologically conforming and of low geometric complexity. To meet the goal of merging a complex non-planar global shell to a local detailed 3D model, an extension of these techniques is proposed to handle meshes of complex shapes that are not only non-matching but also geometrically and topologically non-conforming. The implemented strategy is original and robust: the innovative nature of the approach is to expand the initial local solid model by generating transitional shell meshing. The generated model incorporates two distinct coupling interfaces: (i) non-intrusive global-local coupling and (ii) shell-solid coupling. The multiscale strategy was successfully validated through different numerical experiments using standard Input/Output of a commercial finite element software. In particular, a representative use-case involving a realistic fuselage section of an aircraft was computed.

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On micro–macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials

Cited by 62 publications

References 25 publications

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

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