Adaptivity for clustering-based reduced-order modeling of localized history-dependent phenomena

Ferreira, Bernardo P.; Pires, F.M. Andrade; Bessa, Miguel A.

doi:10.1016/j.cma.2022.114726

Cited by 15 publications

(6 citation statements)

References 78 publications

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“…( 22). For the homogeneous displacement loading conditions (19) the spatial average estimated over both the sufficiently large macrosample w and the indi- (25) coincide with the corresponding averages over the UC…”

Section: Volumetric Boundary Conditions and Mean Fieldsmentioning

confidence: 59%

“…It means that the FEA-clustered method applies the data compression technology by using the k-means clustering, but not the heuristic approach as in TFA. The adaptive clustering-based model proposed in [25] enables the clustering-based domain decomposition to evolve throughout the problem solution, providing optirefinementment in regions where the relevant fields present higher gradients (e.g., in the vicinity of a crack tip).…”

Section: Introductionmentioning

confidence: 99%

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Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Buryachenko¹

2022

Preprint

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In contrast to the classical local theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48:175-–209) is free of any spatial derivatives of the displacement field. A thermoelastic composite materials (CMs) theory with nonlocal peridynamic properties of multiphase constituents of arbitrary geometry is analyzed for periodic structure CMs subjected to the volumetric periodic boundary conditions. Effective properties of peridynamic CM are expressed through the introduced micropolarization tensor averaged over the extended inclusion phase. Decompositions of material and field parameters are performed to analyze the fields produced by both mechanical and eigenfield loading. Transformation field analysis (TFA) and clustering discretization method (defining offline linear stage) adapted to the linear peridynamic micromechanics are proposed by the use of formal similarity of proposed methods with corresponding approaches of local micromechanics. Stress and displacement in each cluster are assumed to be constant and linear functions, respectively, even when a cluster is not a simply connected area in general. This fact greatly reduces the degree of freedom in the problem being considered. The clustering version of TFA for the homogenization of nonlinear peridynamics micromechanics is based on employing eigenstrains to account for inelastic displacements arising from material nonlinearity. The scheme of numerical solution of linear thermoelastic peridynamic problem and estimation of influence functions are presented.

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Section: Volumetric Boundary Conditions and Mean Fieldsmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Buryachenko¹

2022

Preprint

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“…In essence, ROM techniques rely on reducing the dimensionality and complexity of computational models to attain approximate solutions at lower computational cost. In 2017, Bessa and co-workers presented a unified framework for the data-driven analysis of materials [251] and proposed self-consistent clustering ROM, which resulted in subsequent contributions [44,252,253]. Other ROM approaches based on the proper orthogonal decomposition method [254][255][256][257], transformation field analysis [258][259][260], wavelet representation [261], and nonlinear manifolds [262] have gained popularity as well.…”

Section: Hierarchical Methodsmentioning

confidence: 99%

“…Within this context, parallel computing [39], sub-incrementation schemes [40], and adaptive strategies [41,42] have all been studied over the past two decades. Moreover, reduced order modelling has become a hot topic of research, with machine learning techniques [43,44] employed to achieve fast simulations and precise numerical solutions. With this in mind, although multi-scale models are being continuously developed, delving into more complex formulations such as second-order computational homogenisation [45] that can speed up multi-scale simulations has become a focal point for researchers.…”

Section: Multi-scale Modelsmentioning

confidence: 99%

Mechanisms of Component Degradation and Multi-Scale Strategies for Predicting Composite Durability: Present and Future Perspectives

Ferreira Rocha,

Fonseca Gonçalves,

dos Reis

et al. 2024

J. Compos. Sci.

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Composite materials, valued for their adaptability, face challenges associated with degradation over time. Characterising their durability through traditional experimental methods has shown limitations, highlighting the need for accelerated testing and computational modelling to reduce time and costs. This study presents an overview of the current landscape and future prospects of multi-scale modelling for predicting the long-term durability of composite materials under different environmental conditions. These models offer detailed insights into complex degradation phenomena, including hydrolytic, thermo-oxidative, and mechano-chemical processes. Recent research trends indicate a focus on hygromechanical models across various materials, with future directions aiming to explore less-studied environmental factors, integrate multiple stressors, investigate emerging materials, and advance computational techniques for improved predictive capabilities. The importance of the synergistic relationship between experimental testing and modelling is emphasised as essential for a comprehensive understanding of composite material behaviour in diverse environments. Ultimately, multi-scale modelling is seen as a vital contributor to accurate predictions of environmental effects on composite materials, offering valuable insights for sustainable development across industries.

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“…cratepy is essentially a numerical tool for any application that requires material multi-scale simulations. Given the intrinsic clustering-based reduced-order modeling approach (e.g., SCA (Liu et al, 2016), ASCA (Ferreira B. P. et al, 2022)), CRATE is mostly useful in applications where the computational cost of standard simulation methods is prohibitive, namely to solve lower-scales in coupled hierarchical multi-scale simulations (e.g., B. P. Ferreira (2022)) and to generate large material response databases for data-driven frameworks based on machine learning (e.g., Bessa et al (2017)). CROMs achieve a striking balance between accuracy and computational cost by first performing a clustering-based domain decomposition of the material model and then solving the equilibrium problem formulated over the resulting reduced model.…”

Section: Crate (Clustering-based Nonlinear Analysis Of Materialsmentioning

confidence: 99%

CRATE: A Python package to perform fast material simulations

Ferreira,

Pires,

Bessa

2023

JOSS

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Adaptivity for clustering-based reduced-order modeling of localized history-dependent phenomena

Cited by 15 publications

References 78 publications

Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Mechanisms of Component Degradation and Multi-Scale Strategies for Predicting Composite Durability: Present and Future Perspectives

CRATE: A Python package to perform fast material simulations

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