Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials

Kuhn, Jannick; Schneider, Matti; Sonnweber-Ribic, Petra; Böhlke, Thomas

doi:10.1016/j.cma.2020.113175

Cited by 25 publications

(19 citation statements)

References 87 publications

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“…In this section, we consider a closed‐cell foam, see Figure 1B. Following Abdullahi et al, 61 the microstructure was generated by shrinking the cells of a Laguerre tessellation, where we use the Newton algorithm discussed in Kuhn et al 62 to generate 27 Laguerre cells of equal volume. The resulting foam has a volume fraction of

11.6 %

, and was discretized by

12 8^{3}

voxels.…”

Section: Computational Examplesmentioning

confidence: 99%

On non‐stationary polarization methods in FFT‐based computational micromechanics

Schneider

2021

Numerical Meth Engineering

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Polarization-type methods are among the fastest solution methods for FFT-based computational micromechanics. However, their performance depends critically on the choice of the reference material. Only for finitely contrasted materials, optimum-selection strategies are known. This work focuses on adaptive strategies for choosing the reference material, details their efficient implementation, and investigates the computational performance. The case of porous materials is explicitly included. As a byproduct, we introduce a suitable convergence criterion that permits a fair comparison to strain-based FFT solvers and Eyre-Milton type implementations.

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11.6 %

, and was discretized by

12 8^{3}

voxels.…”

Section: Computational Examplesmentioning

confidence: 99%

On non‐stationary polarization methods in FFT‐based computational micromechanics

Schneider

2021

Numerical Meth Engineering

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“…In this section, we investigate a more complex microstructure to demonstrate the capabilities of the approach. For this we use a synthetic microstructure, generated by the method discussed in Kuhn et al (2020), consisting of 100 grains (with equal volume). Furthermore, each grain is randomly assigned a crystalline orientation, s.t.…”

Section: Industrial-scale Polycrystalline Microstructurementioning

confidence: 99%

Identifying material parameters in crystal plasticity by Bayesian optimization

et al. 2021

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In this work, we advocate using Bayesian techniques for inversely identifying material parameters for multiscale crystal plasticity models. Multiscale approaches for modeling polycrystalline materials may significantly reduce the effort necessary for characterizing such material models experimentally, in particular when a large number of cycles is considered, as typical for fatigue applications. Even when appropriate microstructures and microscopic material models are identified, calibrating the individual parameters of the model to some experimental data is necessary for industrial use, and the task is formidable as even a single simulation run is time consuming (although less expensive than a corresponding experiment). For solving this problem, we investigate Gaussian process based Bayesian optimization, which iteratively builds up and improves a surrogate model of the objective function, at the same time accounting for uncertainties encountered during the optimization process. We describe the approach in detail, calibrating the material parameters of a high-strength steel as an application. We demonstrate that the proposed method improves upon comparable approaches based on an evolutionary algorithm and performing derivative-free methods.

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“…As our first example, we consider a polycrystalline microstructure generated synthetically based on Laguerre tessellations and the algorithm described in Kuhn et al [67]. Following a similar approach as Nguyen et al [30] within the context of phase-field fracture, we distinguish between 2D and 3D structures.…”

Section: A Polycrystalline Microstructurementioning

confidence: 99%

“…We consider generated 3D Laguerre tessellations [67] with random grain orientation in each grain. Similar to the 2D case, we vary both the number of grains and the anisotropy factor.…”

Section: Three-dimensional Structuresmentioning

confidence: 99%

Computing the effective crack energy of heterogeneous and anisotropic microstructures via anisotropic minimal surfaces

Ernesti

Schneider

2021

Comput Mech

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A variety of materials, such as polycrystalline ceramics or carbon fiber reinforced polymers, show a pronounced anisotropy in their local crack resistance. We introduce an FFT-based method to compute the effective crack energy of heterogeneous, locally anisotropic materials. Recent theoretical works ensure the existence of representative volume elements for fracture mechanics described by the Francfort–Marigo model. Based on these formulae, FFT-based algorithms for computing the effective crack energy of random heterogeneous media were proposed, and subsequently improved in terms of discretization and solution methods. In this work, we propose a maximum-flow solver for computing the effective crack energy of heterogeneous materials with local anisotropy in the material parameters. We apply this method to polycrystalline ceramics with an intergranular weak plane and fiber structures with transversely isotropic crack resistance.

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Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials

Cited by 25 publications

References 87 publications

On non‐stationary polarization methods in FFT‐based computational micromechanics

On non‐stationary polarization methods in FFT‐based computational micromechanics

Identifying material parameters in crystal plasticity by Bayesian optimization

Computing the effective crack energy of heterogeneous and anisotropic microstructures via anisotropic minimal surfaces

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