Multiscale analysis of elastic-viscoplastic composite using a cluster-based reduced-order model

Ri, Jun-Hyok; Ri, Un-Il; Hong, Hyon-Sik

doi:10.1016/j.compstruct.2021.114209

Cited by 5 publications

(4 citation statements)

References 34 publications

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“…19,[44][45][46] As a drawback, a phenomenological (coupled or uncoupled) model needs to be tailored for each mesoscale model. A cluster-based framework named CNTFA 24 provides an alternative way for the reduced variables to evolve, without the need to derive a specific reduced order model separately.…”

Section: Cluster-based Nonuniform Transformation Field Analysismentioning

confidence: 99%

“…As a drawback, a phenomenological (coupled or uncoupled) model needs to be tailored for each mesoscale model. A cluster‐based framework named CNTFA 24 provides an alternative way for the reduced variables to evolve, without the need to derive a specific reduced order model separately. Given the great variety of constitutive models for bones, 2 we adapt the CNTFA theory for reduced order homogenization of bones.…”

Section: Cluster‐based Nonuniform Transformation Field Analysismentioning

confidence: 99%

“…As suggested in the work, 24 we formulate a least‐squares optimization problem as

[{(Δ ζ_{i})}^{l}, {(Δ ξ_{j})}^{l}] = {argmin}_{([],, normalΔ ζ_{i}, normalΔ ξ_{j})} \frac{{false\sum}_{I = 1}^{K} w^{I} {(||, |{((), normalΔ ε^{p, I})}^{l} - {false\sum}_{i = 1}^{M} {((), normalΔ ζ_{i})}^{l} {bold-italicν}_{i}^{I} - {false\sum}_{j = 1}^{N} {((), normalΔ ξ_{j})}^{l} {bold-italicμ}_{j}^{I}|)}^{2}}{{false\sum}_{I = 1}^{K} {(||, |{(Δ {bold-italicε}^{p, I})}^{l}|)}^{2}},

where,

w^{I}

denotes the volume fraction of the

I

th cluster. The optimization problem (19) has an analytical solution as

{((), normalΔ ζ_{i})}^{l} = {((), \sum_{I = 1}^{K} w_{I} ((), \sum_{i = 1}^{M} ζ_{i}^{I} : ζ_{i}^{I}))}^{- 1} ({false\sum}_{I = 1}^{K} w_{I} ({false\sum}_{i = 1}^{M} {((), normalΔ ε^{p, I})}^{l} : ζ_{i}^{I})),

…”

Section: Cluster‐based Nonuniform Transformation Field Analysismentioning

confidence: 99%

“…20,21 Subsequently, the work 22 proposed a so-called self-consistent clustering analysis (SCCA), where the micro-domain is decomposed into several uniform subdomains via a clustering analysis. The recent works [23][24][25] combined the NTFA with a clustering algorithm and proposed a new cluster-based reduced order model called CNTFA, containing a large variety of mesoscale models in a unified framework. In addition, other MOR techniques include a priori hyperreduction method 26 or proper generalized decomposition.…”

mentioning

confidence: 99%

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Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Ju,

Zhou,

Liang

et al. 2023

Numer Methods Biomed Eng

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We present a reduced order model for efficient nonlinear homogenization of bones, accounting for strength difference effects and containing some well‐known plasticity models (like von Mises or Drucker‐Prager) as special cases. The reduced order homogenization is done by using a cluster‐based model order reduction technique, called cluster‐based nonuniform transformation field analysis. For an offline phase, a space–time decomposition is performed on the mesoscopic plastic strain fields, while a clustering analysis is employed for a spatial decomposition of the mesoscale RVE model. A volumetric‐deviatoric split is additionally introduced to capture the enriched characteristics of the mesoscopic plastic strain fields. For an online analysis, the reduced order model is formulated in a unified minimization problem, which is compatible with a large variety of material models. Both cortical and trabecular bones are considered for numerical experiments. Compared to conventional FE‐based RVE computations, the developed reduced order model renders a considerable acceleration rate beyond , while maintaining a sufficient accuracy level.

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Section: Cluster-based Nonuniform Transformation Field Analysismentioning

confidence: 99%

Section: Cluster‐based Nonuniform Transformation Field Analysismentioning

confidence: 99%

“…As suggested in the work, 24 we formulate a least‐squares optimization problem as

[{(Δ ζ_{i})}^{l}, {(Δ ξ_{j})}^{l}] = {argmin}_{([],, normalΔ ζ_{i}, normalΔ ξ_{j})} \frac{{false\sum}_{I = 1}^{K} w^{I} {(||, |{((), normalΔ ε^{p, I})}^{l} - {false\sum}_{i = 1}^{M} {((), normalΔ ζ_{i})}^{l} {bold-italicν}_{i}^{I} - {false\sum}_{j = 1}^{N} {((), normalΔ ξ_{j})}^{l} {bold-italicμ}_{j}^{I}|)}^{2}}{{false\sum}_{I = 1}^{K} {(||, |{(Δ {bold-italicε}^{p, I})}^{l}|)}^{2}},

where,

w^{I}

denotes the volume fraction of the

I

th cluster. The optimization problem (19) has an analytical solution as

{((), normalΔ ζ_{i})}^{l} = {((), \sum_{I = 1}^{K} w_{I} ((), \sum_{i = 1}^{M} ζ_{i}^{I} : ζ_{i}^{I}))}^{- 1} ({false\sum}_{I = 1}^{K} w_{I} ({false\sum}_{i = 1}^{M} {((), normalΔ ε^{p, I})}^{l} : ζ_{i}^{I})),

…”

Section: Cluster‐based Nonuniform Transformation Field Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Ju,

Zhou,

Liang

et al. 2023

Numer Methods Biomed Eng

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A cluster‐based incremental potential approach for reduced order homogenization of bones

Ju,

Xu,

et al. 2024

Numer Methods Biomed Eng

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We develop a cluster‐based model order reduction (called C‐pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C‐pRBMOR approach includes both a clustering analysis spatially decomposing the micro‐domain within an RVE and a space–time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster‐enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C‐pRBMOR approach. A striking acceleration rate beyond 104 against conventional FE computations and that beyond 103 against the original pRBMOR approach are observed.

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Dimensional reduction technique for the prediction of global and local responses of unidirectional composite with matrix nonlinearity and varying fiber packing geometry

Jamnongpipatkul,

Naets,

Gilabert

2024

Engineering with Computers

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Multiscale analysis of elastic-viscoplastic composite using a cluster-based reduced-order model

Cited by 5 publications

References 34 publications

Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

A cluster‐based incremental potential approach for reduced order homogenization of bones

Dimensional reduction technique for the prediction of global and local responses of unidirectional composite with matrix nonlinearity and varying fiber packing geometry

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