On the micromechanics of deep material networks

Gajek, Sebastian; Schneider, Matti; Böhlke, Thomas

doi:10.1016/j.jmps.2020.103984

Cited by 59 publications

(96 citation statements)

References 61 publications

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“…The presented thermomechanical solver is compatible to the interpolation approach by Köbler et al, 76 enabling the development of effective (macroscopic) surrogate models for arbitrary fiber orientations. For more general structures and material models, thermomechanical FFT-based computations may enter data-driven approaches, such as deep material networks, [77][78][79] to facilitate the simulation of components on the macroscale.…”

Section: Discussionmentioning

confidence: 99%

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

Wicht

Schneider

Böhlke

2020

Int J Numer Methods Eng

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Thermomechanical couplings are present in many materials and should therefore be considered in multiscale approaches. Specific cases of thermomechanical behavior are the isothermal and the adiabatic regime, in which the behavior of real materials differs. Based on the consistent asymptotic homogenization framework for thermomechanically coupled generalized standard materials, the present work is devoted to computing the effective thermomechanical behavior of composite materials in the context of fast Fourier transform (FFT)-based micromechanics. Exploiting the homogeneity of the temperature on the microscale, we develop a fast implicit staggered solution scheme for the coupled problem, which is compatible to existing strain-based micromechanics solvers. Due to its implicit formulation, the algorithm permits large time steps for computations involving strong thermomechanical coupling. We investigate the performance of modern FFT-based algorithms combined with the proposed thermomechanical solution strategy. In this context, the Barzilai-Borwein method is identified as particularly efficient, inducing only a small overhead compared with the traditional isothermal setting. We demonstrate the effectiveness of the presented approach for short-fiber reinforced composites with viscoelastic matrix behavior.

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Section: Discussionmentioning

confidence: 99%

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

Wicht

Schneider

Böhlke

2020

Int J Numer Methods Eng

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“…Possible solutions include the use of sparse sampling techniques [337], tensor methods [338] or AI-based surrogate models [339].…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A review of nonlinear FFT-based computational homogenization methods

Schneider

2021

Acta Mech

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127

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Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.

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“…Once the training process is complete, DMNs can be applied to inelastic problems at finite and infinitesimal strains with impressive accuracy. Subsequently, direct DMNs were introduced by Gajek et al [53,54] which allow for an efficient solution scheme in the inelastic setting as they do not involve additional rotations. Furthermore, Gajek et al [53] motivated the approximation capabilities of (direct) DMNs by showing that, to first-order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization.…”

Section: Introductionmentioning

confidence: 99%

An FE-DMN method for the multiscale analysis of thermomechanical composites

2022

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We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. (Int J Plast 81:18–39, 2016), we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale.

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On the micromechanics of deep material networks

Cited by 59 publications

References 61 publications

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

A review of nonlinear FFT-based computational homogenization methods

An FE-DMN method for the multiscale analysis of thermomechanical composites

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