A constitutive macroscale model for compressible magneto-active polymers based on computational homogenization data: Part I — Magnetic linear regime

Gebhart, Philipp; Wallmersperger, Thomas

doi:10.1016/j.ijsolstr.2021.111294

Cited by 5 publications

(2 citation statements)

References 53 publications

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“…These schemes allow the simulation of engineering components made of materials with underlying microstructure solely based on information about the microstructural arrangement and the properties of the individual components, e. g., matrix and inclusions. Basically, two different types of multiscale schemes exist: the coupled multiscale scheme which is also known as FE 2 approach (finite element square) [13,42,48,49,62,68,69,85] and the decoupled or sequential multiscale scheme [15,27,39,40,67,74,83,84].…”

Section: Multiscale Schemesmentioning

confidence: 99%

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

et al. 2023

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Herein, we present a new data-driven multiscale framework called FE$${}^\textrm{ANN}$$ ANN which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e. g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i. e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered. Thereby, a rather high accuracy could be proved by a validation of the approach.

show abstract

Section: Multiscale Schemesmentioning

confidence: 99%

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

et al. 2023

View full text Add to dashboard Cite

show abstract

“…These schemes allow the simulation of engineering components made of materials with underlying microstructure solely based on information about the microstructural arrangement and the properties of the individual components, e. g., matrix and inclusions. Basically, two different types of multiscale schemes exist: the coupled multiscale scheme which is also known as FE 2 approach (finite element square) [1,2,3,4,5,6,7,8] and the decoupled or sequential multiscale scheme [9,10,11,12,13,14].…”

Section: Multiscale Schemesmentioning

confidence: 99%

FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

Kalina¹,

Linden²,

Brummund³

et al. 2022

Preprint

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Herein, we present a new data-driven multiscale framework called FE ANN which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e. g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i. e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element (FE) simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered. Thereby, a rather high accuracy could be proved by a validation of the approach.

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On some energy‐based variational principles in non‐dissipative magneto‐mechanics using a vector potential approach

Gebhart,

Wallmersperger

2024

Numerical Meth Engineering

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This contribution covers the variational‐based modeling of non‐dissipative magneto‐mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence‐free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re‐entrant corners.

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A constitutive macroscale model for compressible magneto-active polymers based on computational homogenization data: Part I — Magnetic linear regime

Cited by 5 publications

References 53 publications

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

On some energy‐based variational principles in non‐dissipative magneto‐mechanics using a vector potential approach

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