Scale selection in nonlinear fracture mechanics of heterogeneous materials

Akbari, Ahmad; Kerfriden, Pierre; Bordas, Stéphane Pierre Alain

doi:10.1080/14786435.2015.1061716

Cited by 23 publications

(11 citation statements)

References 53 publications

(69 reference statements)

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“…The interested reader is referred to the work of Kerfriden and coworkers and the publications therein, where Newton–Krylov [ 23 ], local–global [ 24 ] domain-wise model order reduction [ 25 ], and Bayesian approaches [ 26 ] are proposed. Those algebraic-based model order reduction techniques may be complemented by multiscale approaches, as in [ 27 ], where a scale-selection approach is proposed for determining the optimal model for a given region. Finally, statistical-based approaches have been proposed [ 28 ] in order to determine the fracture process zone based on the lack of ability of reduced order models to represent the failure of the system.…”

Section: Introductionmentioning

confidence: 99%

Multiple crack detection in 3D using a stable XFEM and global optimization

2018

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A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.

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Section: Introductionmentioning

confidence: 99%

Multiple crack detection in 3D using a stable XFEM and global optimization

2018

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“…This enables the coarsening of the mesh if the discretization error is unnecessarily small in comparison to the modeling error as is done, e.g. in [5] and [120,23,121,118,122] for adaptive scale selection. Conversely, for specific applications where modeling errors are small or moderate, the mesh can be refined efficiently to increase the precision.…”

Section: Applicability For Patient-specific Biomechanics?mentioning

confidence: 99%

Quantifying discretization errors for soft tissue simulation in computer assisted surgery: A preliminary study

Duprez

Bordas

Bucki³

et al. 2020

Applied Mathematical Modelling

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Errors in biomechanics simulations arise from modeling and discretization. Modeling errors are due to the choice of the mathematical model whilst discretization errors measure the impact of the choice of the numerical method on the accuracy of the approximated solution to this specific mathematical model. A major source of discretization errors is mesh generation from medical images, that remains one of the major bottlenecks in the development of reliable, accurate, automatic and efficient personalized, clinically-relevant Finite Element (FE) models in biomechanics. The impact of mesh quality and density on the accuracy of the FE solution can be quantified with a posteriori error estimates. Yet, to our knowledge, the relevance of such error estimates for practical biomechanics problems has seldom been addressed, see [25]. In this contribution, we propose an implementation of some a posteriori error estimates to quantify the discretization errors and to optimize the mesh. More precisely, we focus on error estimation for a user-defined quantity of interest with the Dual Weighted Residual (DWR) technique. We test its applicability and relevance in two situations, corresponding to computations for a tongue and an artery, using a simplified setting, i.e., plane linearized elasticity with contractility of the soft-tissue modeled as a pre-stress. Our results demonstrate the feasibility of such methodology to estimate the actual solution errors and to reduce them economically through mesh refinement.

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“…With increasing computational power, numerical models that fully resolve the microstructural geometry in the whole macroscopic domain, e.g. [5,6], or in regions of interest [7,8], have emerged, addressing problems without clear scale separation.…”

Section: Introductionmentioning

confidence: 99%

“…Influence of morphing operations on resulting (a) two-and (b) three-dimensional geometry. From the original particle distribution (depicted with light grey), the closed-cell, foam-like geometry (shown in blue) is obtained by Eq (7). and the open-like features (plotted in red) follow from Eq (8)…”

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confidence: 99%

Level-set Based Design of Wang Tiles for Modelling Complex Microstructures

Doškář

Zeman

Rypl

et al. 2020

Computer-Aided Design

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Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s unified framework, developed originally for generating particulate and foam-like microstructural geometries of Periodic Unit Cells, to non-periodic microstructural representations based on the formalism of Wang tiles. This formalism has been recently proposed in order to generalize the Periodic Unit Cell approach, enabling a fast synthesis of arbitrarily large, stochastic microstructural samples from a handful of domains with predefined microstructural compatibility constraints. However, a robust procedure capable of designing complex, three-dimensional, foam-like and cellular morphologies of Wang tiles has not yet been proposed. This contribution fills the gap by significantly broadening the applicability of the tiling concept.Since the original Sonon et al.'s framework builds on a random sequential addition of particles enhanced with an implicit representation of particle boundaries by the level-set field, we first devise an analysis based on a connectivity graph of a tile set, resolving the question where a particle should be copied when it intersects a tile boundary. Next, we introduce several modifications to the original algorithm that are necessary to ensure microstructural compatibility in the generalized periodicity setting of Wang tiles. Having established a universal procedure for generating tile morphologies, we compare strictly aperiodic and stochastic sets with the same cardinality in terms of reducing the artificial periodicity in reconstructed microstructural samples. We demonstrate the superiority of the vertex-defined tile sets for two-dimensional problems and illustrate the capabilities of the algorithm with two-and three-dimensional examples.

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Scale selection in nonlinear fracture mechanics of heterogeneous materials

Cited by 23 publications

References 53 publications

Multiple crack detection in 3D using a stable XFEM and global optimization

Multiple crack detection in 3D using a stable XFEM and global optimization

Quantifying discretization errors for soft tissue simulation in computer assisted surgery: A preliminary study

Level-set Based Design of Wang Tiles for Modelling Complex Microstructures

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