Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling

Yu, Chan; Nezamabadi, Saeid; Zahrouni, Hamid; Yvonnet, Julien

doi:10.1002/nme.4927

Cited by 29 publications

(19 citation statements)

References 27 publications

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“…Furthermore, most discoveries in this paper actually exist elsewhere in various previous publications [12][13][14][15][16]; however, it is useful to provide a more systematic explanation for mechanics-based homogenization. Another important point is that theoretically the mathematical asymptotic homogenization process requires the micro-cell to be small or infinitely small to assume convergence of the process, but this is not necessary for mechanics-based homogenization.…”

Section: Introductionmentioning

confidence: 85%

Homogenization Method for Designing Novel Architectured Cellular Materials

Ma¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Two types of novel architectured cellular materials have been developed [1,2]. To estimate the effective material properties and to optimally design such materials, a suitable homogenization method was needed. An existing asymptotic homogenization process has provided an effective means for the multiscale modeling of continuum solids; however, that method was not easily adapted to the aforementioned materials, which are naturally discrete systems. First, we developed a strain-based homogenization method equivalent to the existing asymptotic homogenization method, but it was developed based on an engineering approach rather than on a mathematical approach such as the one used in asymptotic homogenization. The new approach separates the strain field into a homogenized strain field and a strain variation field in the local cellular domain superposed on the homogenized strain field. The Principle of Virtual Displacements for the relationship between the strain variation field and the homogenized strain field is then used to condense the strain variation field onto the homogenized strain field, and the homogenization process becomes a coordinate reduction process comparable to the Guyan Reduction used in structural dynamics analyses. The characteristic modes and the stress recovery process are also discussed. The new method is then extended to a stress-based homogenization process based on the Principle of Virtual Forces, and it is further applied to address the discrete systems of the aforementioned architectured cellular materials.

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Section: Introductionmentioning

confidence: 85%

Homogenization Method for Designing Novel Architectured Cellular Materials

Ma¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…for more details on multiscale modeling of failure, damage, and crack propagation and Refs. [430] and [447][448][449][450][451][452][453][454][455][456] for background on modeling instability phenomena such as buckling in the context of multiscale modeling.…”

Section: Beyond Purely Elastic Problemsmentioning

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

183

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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“…The RVEs are homogenized in the (shell) plane and integrated through their thickness. This method enables nonlinear CH for shell-type continua (Geers et al, 2007;Coenen et al, 2010;Cong et al, 2015).…”

Section: Nonlinear Computational Homogenizationmentioning

confidence: 99%

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Geers

Kouznetsova

Matouš

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

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Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling

Cited by 29 publications

References 27 publications

Homogenization Method for Designing Novel Architectured Cellular Materials

Homogenization Method for Designing Novel Architectured Cellular Materials

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

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

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