Merits and limits of a variational definition of the effective toughness of heterogeneous materials

Michel, Jean‐Claude; Suquet, Pierre

doi:10.1016/j.jmps.2022.104889

Cited by 11 publications

(2 citation statements)

References 49 publications

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“…A similar approach has been proposed by Willot [73] who investigated the related problem of finding the effective conductivity of resistor networks. Michel-Suquet [74] proposed a different approach to computing the effective crack energy.…”

Section: Computational Approach For Periodic Boundary Conditions-mini...mentioning

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: Computational Approach For Periodic Boundary Conditions-mini...mentioning

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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“…Let us quote for instance Chen et al (2019); Ma and Sun (2020); Li et al (2012); Sharma et al (2018) which put in place fast-fourier transform computations for a phase field modelling of damage. One can also refers to Schneider (2019); Hossain et al (2014); Michel and Suquet (2022) that tackle the problem of the estimation of the effective toughness of heterogeneous materials. With the exception of Chen et al (2022) which will be discussed later, no attempt has been made to determine by mean field homogenisation the effective response of a composite where the onset of damage and its propagation throughout one of the phases is assessed by a damage model, making it nonlinear and, above all, time dependent as the evolution versus time of the damage is sought.…”

Section: Introductionmentioning

confidence: 99%

A mean-field micromechanical incremental approach for brittle damage in particulate microstructures under monotonic loading, using a piecewise uniform damage field

Gauthier,

Masson,

Gărăjeu

et al. 2023

International Journal of Solids and Structures

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Accounting for weak interfaces in computing the effective crack energy of heterogeneous materials using the composite voxel technique

Ernesti

Schneider

2023

Arch Appl Mech

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We establish a computational methodology to incorporate interfaces with lower crack energy than the surrounding phases when computing the effective crack energy of brittle composite materials. Recent homogenization results for free discontinuity problems are directly applicable to the time-discretized Francfort-Marigo model of brittle fracture in the anti-plane shear case, and computational tools were introduced to evaluate the effective crack energy on complex microstructures using FFT-based solvers and a discretization scheme based on a combinatorially consistent grid. However, this approach only accounts for the crack resistance per volume and is insensitive to the crack resistance of the interface which is expected to play a significant role by considerations from materials science. In this work we introduce a remedy exploiting laminate composite voxels. The latter were originally introduced to enhance the accuracy of solutions for elasticity problems on regular voxel grids. We propose an accurate approximation of the effective crack energy of a laminate with weak interface where an explicit solution is available. We incorporate this insight into an efficient algorithmic framework. Finally, we demonstrate the capabilities of our approach on complex microstructures with weak interfaces between different constituents.

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Merits and limits of a variational definition of the effective toughness of heterogeneous materials

Cited by 11 publications

References 49 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

A mean-field micromechanical incremental approach for brittle damage in particulate microstructures under monotonic loading, using a piecewise uniform damage field

Accounting for weak interfaces in computing the effective crack energy of heterogeneous materials using the composite voxel technique

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