Multiscale aggregating discontinuities: A method for circumventing loss of material stability

Belytschko, Ted; Löhnert, Stefan; Song, Jeong‐Hoon

doi:10.1002/nme.2156

Cited by 209 publications

(159 citation statements)

References 46 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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“…The displacement jump across S is denoted: β(x, t). The regular macro-strain ε R is defined in points excluding S, and is written in equation (2). Hence, from (1) and (2), observe that the macro-displacement and macro-strain fields are completely described through the variables: (u, β).…”

Section: (A) (B)mentioning

confidence: 99%

“…This methodological approach has been the subject of recent intensive research in the scientific community. A number of novel contributions have been made in this direction, see for example the approaches of Matous et al [21], Verhoosel et al [44], Nguyen et al [27,29] Belytschko and coworkers [2,41], Geers and coworkers [6], Unger [43] and Souza et al [42]. However, the development of a consistent method has remained full of major theoretical challenges.…”

Section: Introductionmentioning

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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“…In [18,1], the authors have developed the MAD (Multiscale Aggregating Discontinuities) method in which a macroscopic crack is determined as equivalent to a bunch of microscale cracks. The method is however restricted to cases where the separation-of-scales principle is violated for the micro sample had to match the macro element to which it is linked.…”

Section: Introductionmentioning

confidence: 99%

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Nguyen

Lloberas-Valls

Stroeven

et al. 2011

Computer Methods in Applied Mechanics and Engineering

137

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The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction-separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE 2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method.

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Multiscale aggregating discontinuities: A method for circumventing loss of material stability

Cited by 209 publications

References 46 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

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

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