A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

Suzuki, Jorge L.; Tuttle, Tyler G.; Roccabianca, Sara; Zayernouri, Mohsen

doi:10.3390/fractalfract5040223

Cited by 10 publications

(9 citation statements)

References 73 publications

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“…To identify the parameters for the two‐branch FMG model illustrated in Figure 1, we employ a global optimization method, more specifically the particle‐swarm optimization (PSO) algorithm, 56 which has been recently employed in the parameter identification of linear and non‐linear fractional operators for soft media 57 . We utilize a population of

N_{pop} = 200

individuals, and

N_{it} = 10000

iterations for each optimization run, and due to the stochastic nature of the PSO algorithm, we perform 10 optimization runs and report the expected values and standard deviation for each of the identified material parameters.…”

Section: Methodsmentioning

confidence: 99%

Experimental and modeling studies of IPDI‐based polyurea elastomers – The role of hard segment fraction

Tzelepis

Suzuki

et al. 2023

J of Applied Polymer Sci

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Segmented polyureas (PUa) are industrially important class of polymers widely used in coatings, sealant, and adhesive applications. Here, we report synthesis, characterization, and modeling of Isophorone Diisocyanate-Diethyl-Toluene-Diamine-Polyether amine (IPDI-DETDA-PO PUa) with varied hard segment contents of 20, 30, and 40 weight percent. For each of the three materials, we study its structure and phase behavior using FTIR, DSC, and TEM, and clearly show the presence of microphase separation between the hard and soft nanodomains. We then measure the linear viscoelastic response of the PUa-s using DMA (frequency sweeps at multiple temperatures). The DMA data are shown to obey the time-temperature superposition. Finally, we develop a new micromechanical model describing the DMA results; the model describes a phaseseparated PUa as two "Fractional-order Maxwell gels" branches, connected in parallel, with the first FMG branch representing the "percolated hard phase" and the second one modeling the "filled soft phase". In agreement with the earlier thermodynamic theories, the volume-fraction of the percolated hard phase is related to the hard segment weight-fraction (HSWF), defined as the combined mass of IPDI and DETDA normalized to the total mass of the polymer. The data and model are found to be in a good qualitative and quantitative agreement.adhesive, dynamic mechanical analysis, fractional calculus, hard domains, polyurea, time temperature superposition | INTRODUCTIONPolyurethanes (PU), polyureas (PUa), and poly (urethaneureas) (PUU) represent a fascinating family of polymers. [1][2][3][4] Their applications include coatings, 5 adhesives and sealants, 6,7 elastomers, 8 as well as rigid foams for thermal insulation 9 and flexible foams for furnishings

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N_{pop} = 200

individuals, and

N_{it} = 10000

Section: Methodsmentioning

confidence: 99%

Experimental and modeling studies of IPDI‐based polyurea elastomers – The role of hard segment fraction

Tzelepis

Suzuki

et al. 2023

J of Applied Polymer Sci

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“…We also observe that the limit cases are given by G F M ∼ t −β1 as t → 0 and G F M ∼ t −β2 as t → ∞, indicating that the FM model provides a behavior transitioning from slowerto-faster relaxation. We refer the reader to [3,13,37] for a number of applications of the aforementioned models. We should notice that both FKV and FM models are able to recover the SB element with a convenient set of pseudo-constants and…”

Section: Definitions Of Fractionalmentioning

confidence: 99%

“…Introduction. Power law behavior has been observed in living cells [9,22] and bio-tissues [12,21,37]. This stems from the ubiquitous self-similar and scale-free nature of the tissue/cell microstructure, which can be physically and mathematically scaled up to continuum level, manifesting in the power law behavior in the lumped sense.…”

mentioning

confidence: 99%

“…This stems from the ubiquitous self-similar and scale-free nature of the tissue/cell microstructure, which can be physically and mathematically scaled up to continuum level, manifesting in the power law behavior in the lumped sense. Such power law relationships have been seen in auditory hair cells, positioned in the sensory organ of hearing, cochlea [18], vocal fold tissues [5], and bladder tissues [37]. Experimental evidence suggests that complex material behavior may possess more than a single power-law scaling in the viscoelastic regime, particularly in multifractal structures, such as in cells [28] and biological tissues [38], due to their complex, hierarchical and heterogeneous microstructures.For such cases, a single fractional rheological element is not sufficient to capture the observed behavior even if the data suggest a linear viscoelastic behavior.…”

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confidence: 99%

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A General Return-Mapping Framework for Fractional Visco-Elasto-Plasticity

Suzuki¹,

Naghibolhosseini²,

Zayernouri³

2022

Preprint

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We develop a fractional return-mapping framework for power-law visco-elastoplasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known fractional linear viscoelastic models, such as Kelvin-Voigt, Maxwell, Kelvin-Zener and Poynting-Thomson. We also consider a fractional quasilinear version of Fung's model to account for stress/strain nonlinearity. The fractional viscoelastic models are combined with a fractional visco-plastic device, coupled with fractional viscoelastic models involving serial combinations of Scott-Blair elements. We then develop a general return-mapping procedure, which is fully implicit for linear viscoelastic models, and semi-implicit for the quasi-linear case. We find that, in the correction phase, the discrete stress projection and plastic slip have the same form for all the considered models, although with different property and time-step dependent projection terms. A series of numerical experiments is carried out with analytical and reference solutions to demonstrate the convergence and computational cost of the proposed framework, which is shown to be at least first-order accurate for general loading conditions. Our numerical results demonstrate that the developed framework is more flexible, preserves the numerical accuracy of existing approaches while being more computationally tractable in the visco-plastic range due to a reduction of 50% in CPU time. Our formulation is especially suited for emerging applications of fractional calculus in bio-tissues that present the hallmark of multiple viscoelastic power-laws coupled with visco-plasticity.

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“…2016; Yu, Perdikaris & Karniadakis 2016; Failla & Zingales 2020; Suzuki et al. 2021 a , b , c ), modelling the near-wall turbulence (Keith, Khristenko & Wohlmuth 2021) and Reynolds-averaged Navier–Stokes modelling for wall-bounded turbulent flows (Mehta et al. 2019; Song & Karniadakis 2021) and subfilter modelling for large-eddy simulation (LES) of turbulence (Samiee, Akhavan-Safaei & Zayernouri 2020; Akhavan-Safaei, Samiee & Zayernouri 2021; Di Leoni et al.…”

Section: Introductionmentioning

confidence: 99%

A non-local spectral transfer model and new scaling law for scalar turbulence

Akhavan-Safaei

Zayernouri

2023

J. Fluid Mech.

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In this study, we revisit the spectral transfer model for the turbulent intensity in passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using a fractional-order Laplacian operator that facilitates the robust inclusion of the non-local effects originating from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide an a priori estimate for the non-local model based on the scaling analysis of the scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of the scalar gradient and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the non-local model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for large-eddy simulation (Akhavan-Safaei et al., J. Comput. Phys., vol. 446, 2021, 110571) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model.

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A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

Cited by 10 publications

References 73 publications

Experimental and modeling studies of IPDI‐based polyurea elastomers – The role of hard segment fraction

Experimental and modeling studies of IPDI‐based polyurea elastomers – The role of hard segment fraction

A General Return-Mapping Framework for Fractional Visco-Elasto-Plasticity

A non-local spectral transfer model and new scaling law for scalar turbulence

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