A decoupling scheme for two‐scale finite thermoviscoelasticity with thermal and cure‐induced deformations

Saito, Ryosuke; Yamanaka, Yosuke; Matsubara, Seishiro; Okabe, Tomonaga; Moriguchi, Shuji; Terada, Kenjiro

doi:10.1002/nme.6575

Cited by 13 publications

(4 citation statements)

References 58 publications

(157 reference statements)

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“…Considering that the main purpose is to validate efficiency and accuracy of the proposed multiscale model, the hexagonal fiber arrangement is here adopted, which has been widely used in previously studies. 18,24,25,30,41 In this study, the fiber volume fraction of the composites is assumed to be 52% and the diameter of fiber is 7.0 μm. The interphase is here modeled, which plays an essential role in transferring the stress and deformation between fiber and resin.…”

Section: Model Illustrationmentioning

confidence: 99%

“…To overcome the above mentioned high computational cost, Saito et al developed an uncoupled multiscale model based on the resolved-scale method combined with the viscoelastic constitutive model to investigate the curing-residual stresses of composite laminates, in which the macroscopic stresses were obtained by averaging the microscopic stresses. 30 Hui et al used this uncoupled multiscale model to obtain the residual stress of the polymer matrix and optimized the process to reduce the tensile curing residual stresses of the resin of a composite laminate, 31 for which a plane-stress model was constructed for the microscopic RVE to reduce the computational cost. However, it is still very time-consuming to obtain the full filed microscopic residual stress by directly using the resolved scale method, especially for threedimension modeling and optimization of large engineering composite parts.…”

Section: Introductionmentioning

confidence: 99%

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An efficient viscoelastic multiscale model for investigation on the cure‐induced microscopic residual stresses of composite laminates

Liu,

Cao

et al. 2024

Polymer Composites

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The cure‐induced residual stresses have a significant influence on the deformation and mechanical properties of composites. Moreover, the cure‐induced residual stresses exhibit multi‐level and multiscale distributions due to the complexity of micro‐structure of composites and anisotropic characteristics. In this paper, a computationally efficient multiscale procedure is proposed to predict the microscopic residual stresses induced by cure temperature, cure shrinkage and macroscopic residual stresses, which is based to the linear viscoelastic theory combined with the micro‐mechanics method. The instantaneous microscopic residual stresses are expressed as a linear combination of the instantaneous temperature increment, degree of cure increment and macroscopic strain increment at all times of the cure process until to the current time. The proposed method is verified in comparison with the published results in literature and the microscale FEA at different length scales, respectively. The results show that the proposed method is about a thousand times faster than directly using FEA in the microscale RVE model once the influence coefficient matrices are determined. At length, the microscale stresses of all nodes of the entire macroscale model are examined by using the proposed method. It is found that the thermal‐chemical‐mechanical loads lead to serious microscopic stresses for the matrix and interphase constituents, especially for those due to the macroscopic residual stresses.Highlights Microscale residual stress is written as a linear combination of macroscale loads. Applying macroscale loads on microscale FEA model to obtain influence matrices. The presented model avoids repeatedly FEA microscopic to improve the efficiency. The online time required for the proposed model is much less than microscale FEA. The microscale stress increases the risk of matrix cracking and interface bonding.

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Section: Model Illustrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient viscoelastic multiscale model for investigation on the cure‐induced microscopic residual stresses of composite laminates

Liu,

Cao

et al. 2024

Polymer Composites

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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.

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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) [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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A decoupling scheme for two‐scale finite thermoviscoelasticity with thermal and cure‐induced deformations

Cited by 13 publications

References 58 publications

An efficient viscoelastic multiscale model for investigation on the cure‐induced microscopic residual stresses of composite laminates

An efficient viscoelastic multiscale model for investigation on the cure‐induced microscopic residual stresses of composite laminates

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

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