Fast Reconstruction of Microstructures with Ellipsoidal Inclusions Using Analytical Descriptors

Seibert, Paul; Husert, Markus; Wollner, Maximilian P.; Kalina, Karl A.; Kästner, Markus

doi:10.1016/j.cad.2023.103635

Cited by 5 publications

(1 citation statement)

References 66 publications

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“…This is known as DMCR [25,26], which is implemented in the MCRpy software [34] and is validated in Seibert et al [33]. Some recent approaches in the literature can be identified as special cases of DMCR [35][36][37][38].…”

Section: Motivationmentioning

confidence: 99%

On the relevance of descriptor fidelity in microstructure reconstruction

Seibert,

Raßloff,

Kalina

et al. 2023

Proc Appl Math and Mech

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A common strategy for reducing the computational effort of descriptor‐based microstructure reconstruction in the Yeong–Torquato algorithm lies in restricting the choice of descriptors to an efficiently computable subset. As an alternative, the number of iterations can be reduced by gradient‐based optimization as in differentiable microstructure characterization and reconstruction (DMCR). This allows for, but does not require, the use of a set of informative, high‐dimensional and computationally expensive descriptors that would be unfeasible for a high number of iterations. For this reason, the present work investigates the role of descriptor fidelity on microstructure reconstruction results. More precisely, spatial two‐ and three‐point correlations as well as the lineal path function are computed on 2D planes as well as on 1D lines. These descriptors are used for reconstruction with the Yeong–Torquato and DMCR algorithm and the results are compared throughout various microstructures, respectively.

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Section: Motivationmentioning

confidence: 99%

On the relevance of descriptor fidelity in microstructure reconstruction

Seibert,

Raßloff,

Kalina

et al. 2023

Proc Appl Math and Mech

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Fast descriptor-based 2D and 3D microstructure reconstruction using the Portilla–Simoncelli algorithm

Seibert,

Raßloff,

Kalina

et al. 2024

Engineering with Computers

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Reconstructing microstructures from statistical descriptors is a key enabler of computer-based inverse materials design. In the Yeong–Torquato algorithm and other common methods, the problem is approached by formulating it as an optimization problem in the space of possible microstructures. In this case, the error between the desired microstructure and the current reconstruction is measured in terms of a descriptor. As an alternative, descriptors can be regarded as constraints defining subspaces or regions in the microstructure space. Given a set of descriptors, a valid microstructure can be obtained by sequentially projecting onto these subspaces. This is done in the Portilla–Simoncelli algorithm, which is well known in the field of texture synthesis. Noting the algorithm’s potential, the present work aims at introducing it to microstructure reconstruction. After exploring its capabilities and limitations in 2D, a dimensionality expansion is developed for reconstructing 3D volumes from 2D reference data. The resulting method is extremely efficient, as it allows for high-resolution reconstructions on conventional laptops. Various numerical experiments are conducted to demonstrate its versatility and scalability. Finally, the method is validated by comparing homogenized mechanical properties of original and reconstructed 3D microstructures.

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Statistical analysis of effective crack properties by microstructure reconstruction and phase-field modeling

Seibert,

Hirsch,

Kluge

et al. 2024

Arch Appl Mech

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Understanding the relation between the microstructure and the material’s effective behavior is an important aspect in inverse computational materials engineering. Especially in the context of localized, inelastic phenomena like plasticity and crack growth, the microstructure morphology plays a crucial role. Due to the stochastic nature of heterogeneous media, a statistical analysis over multiple simulations is necessary, since even with the same material, the simulated crack paths and effective crack lengths are highly dependent on the specific locations of microstructural features. A relevant factor that limits this type of investigation is the high cost of real microstructure data. This work presents a digital workflow for exploring the fracture properties of materials. Therein, the required statistical analyses are facilitated by an algorithm that reconstructs multiple realization of a material structure given a single example. The reconstructed structures are discretized with a regular non-conforming mesh with a diffuse interface and crack representation. Crack phase-field simulations are conducted in order to analyze the effective response. An in-depth introduction to the required methods is given together with a statistical evaluation of the conducted numerical experiments. It is concluded that the statistical variation of the effective material behavior overshadows morphological trends in the presented case. This confirms the relevance and utility of complementing simulation-based workflows with microstructure reconstruction and statistical analyses.

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Fast Reconstruction of Microstructures with Ellipsoidal Inclusions Using Analytical Descriptors

Cited by 5 publications

References 66 publications

On the relevance of descriptor fidelity in microstructure reconstruction

On the relevance of descriptor fidelity in microstructure reconstruction

Fast descriptor-based 2D and 3D microstructure reconstruction using the Portilla–Simoncelli algorithm

Statistical analysis of effective crack properties by microstructure reconstruction and phase-field modeling

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