On image analysis and micromechanics

Jeulin, Dominique

doi:10.1051/rphysap:01988002304054900

Cited by 13 publications

(6 citation statements)

References 5 publications

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“…For the non-axis aligned case, the cut field wraps around the microstructure several times in order to both preserve the mean normal of the cut and to retain periodicity. Thus, at least for the axis-aligned case, it appears reasonable the minimum cut may be computed by an algorithm which returns a (weighted) shortest path [75][76][77]. Indeed, after fixing two corresponding points on opposing edges of the microstructure, a minimum weighted path joining the two points would have to be computed.…”

Section: From Minimum Cut To Shortest Path Problemsmentioning

confidence: 99%

Investigations on the influence of the boundary conditions when computing the effective crack energy of random heterogeneous materials using fast marching methods

2022

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Recent stochastic homogenization results for the Francfort–Marigo model of brittle fracture under anti-plane shear indicate the existence of a representative volume element. This homogenization result includes a cell formula which relies on Dirichlet boundary conditions. For other material classes, the boundary conditions do not effect the effective properties upon the infinite volume limit but may have a strong influence on the necessary size of the computational domain. We investigate the influence of the boundary conditions on the effective crack energy evaluated on microstructure cells of finite size. For periodic boundary conditions recent computational methods based on FFT-based solvers exploiting the minimum cut/maximum flow duality are available. In this work, we provide a different approach based on fast marching algorithms which enables a liberal choice of the boundary conditions in the 2D case. We conduct representative volume element studies for two-dimensional fiber reinforced composite structures with tough inclusions, comparing Dirichlet with periodic boundary conditions.

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Section: From Minimum Cut To Shortest Path Problemsmentioning

confidence: 99%

Investigations on the influence of the boundary conditions when computing the effective crack energy of random heterogeneous materials using fast marching methods

2022

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“…Based on the principle of Fermat, they were developed with efficient algorithms to estimate effective physical properties related to propagation phenomena [34][35][36]: crack propagation based on a minimal fracture energy criterion [34,36]; diffusion of a product in a composite material [35], sound velocity and fluid invasion in porous media [37]. Based on the principle of Fermat, they were developed with efficient algorithms to estimate effective physical properties related to propagation phenomena [34][35][36]: crack propagation based on a minimal fracture energy criterion [34,36]; diffusion of a product in a composite material [35], sound velocity and fluid invasion in porous media [37].…”

Section: Change Of Scale and Simulationsmentioning

confidence: 99%

Geostatistics for the Next Century

Ziegel¹,

Dimitrakopoulos²

1994

Quantitative Geology and Geostatistics

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“…Minimizing the fracture energy has been considered earlier by Jeulin 61 for predicting crack propagation on two‐dimensional micrographs. In fact, in two spatial dimension, the problem of computing the effective crack energy simplifies drastically.…”

Section: Introductionmentioning

confidence: 99%

A fast Fourier transform based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

Ernesti

Schneider

2021

Numerical Meth Engineering

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This work is concerned with computing the effective crack energy of periodic and random media which arises in mathematical homogenization results for the Francfort-Marigo model of brittle fracture. A previous solver based on the fast Fourier transform (FFT) led to solution fields with ringing or checkerboard artifacts and was limited in terms of the achievable accuracy. As computing the effective crack energy may be recast as a continuous maximum flow problem, we suggest using the combinatorial continuous maximum flow discretization introduced by Couprie et al. The latter is devoid of artifacts, but lacks an efficient large-scale solution method. We fill this gap and introduce a novel solver which relies upon the FFT and a doubling of the local degrees of freedom which is resolved by the alternating direction method of multipliers (ADMM). Last but not least we provide an adaptive strategy for choosing the ADMM penalty parameter, further speeding up the solution procedure. We demonstrate the salient features of the proposed approach on problems of industrial scale.

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On image analysis and micromechanics

Cited by 13 publications

References 5 publications

Investigations on the influence of the boundary conditions when computing the effective crack energy of random heterogeneous materials using fast marching methods

Investigations on the influence of the boundary conditions when computing the effective crack energy of random heterogeneous materials using fast marching methods

Geostatistics for the Next Century

A fast Fourier transform based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

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