Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction

Miehé, Christian; Schröder, Jörg; Becker, Martin

doi:10.1016/s0045-7825(02)00391-2

Cited by 167 publications

(112 citation statements)

References 27 publications

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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

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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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

185

138

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“…We call this scheme, the Classical Multiscale Model (ClaMM). In fact, this procedure follows a standard model widely known in the literature (see Miehe et al [24], Michel et al [22], de Souza et al [7,8], Peric et al [35], and references cited therein). In the second case, item 4.2, the homogenization technique determines the tractions T as a function of the displacement jump β by means of the procedure described in Box 3.…”

Section: Scale Transition Modelsmentioning

confidence: 99%

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

Toro

Sánchez

Huespe

et al. 2013

Numerical Meth Engineering

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In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation (FOMF) devised for modeling failure in heterogeneous materials is described.The proposed model considers two well separated physical length scales, namely: (i) the "macro" scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the "micro" scale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE). On the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the micro scale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE subdomains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to preserve "objectivity" of the homogenized response with respect to the micro-cell size.In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level.Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solution furnished by the two-scale model with respect to a mono-scale Direct Numerical Simulation (DNS) approach.

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“…The more general problem of structural stability of heterogeneous materials and the influence of scale has also been examined recently by Miehe, et al 4 Extending down to the microscale, this study examined periodic, finescale material structures using a scaled continuum approach. This coupled, macro-to-micro approach revealed that one of the primary modeling obstacles was the selection of the relevant size of the representative volume element.…”

Section: American Institute Of Aeronautics and Astronauticsmentioning

confidence: 99%

Predicting the Influence of Nano-scale Material Structure on the In-plane Buckling of Orthotropic Plates

Gates¹,

Odegard²,

Nemeth³

et al. 2004

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics &Amp;amp; Materials Conference

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A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the nonfunctionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system. I. IntroductionDevelopment of high-stiffness and high-strength materials is an important part of the quest to advance aerospace vehicle structures. As a relatively new class of materials, single-walled carbon nanotube (SWNT) -reinforced polymer composites provide many opportunities to demonstrate the performance potential of nanostructured materials for use in structural applications. In particular, SWNT materials have demonstrated the potential for order-of-magnitude increases in strength and stiffness relative to standard carbon-fibers used in typical polymeric composites.

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Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction

Cited by 167 publications

References 27 publications

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

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

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

Predicting the Influence of Nano-scale Material Structure on the In-plane Buckling of Orthotropic Plates

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