Search for: All records

Abstract 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 phase‐separated 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. 

Polyurethane and polyurea-based adhesives are widely used in various applications, from automotive to electronics and medical applications. The adhesive performance depends strongly on its composition, and developing the formulation–structure–property relationship is crucial to making better products. Here, we investigate the dependence of the linear viscoelastic properties of polyurea nanocomposites, with an IPDI-based polyurea (PUa) matrix and exfoliated graphene nanoplatelet (xGnP) fillers, on the hard-segment weight fraction (HSWF) and the xGnP loading. We characterize the material using scanning electron microscopy (SEM) and dynamic mechanical analysis (DMA). It is found that changing the HSWF leads to a significant variation in the stiffness of the material, from about 10 MPa for 20% HSWF to about 100 MPa for 30% HSWF and about 250 MPa for the 40% HSWF polymer (as measured by the tensile storage modulus at room temperature). The effect of the xGNP loading was significantly more limited and was generally within experimental error, except for the 20% HSWF material, where the xGNP addition led to about an 80% increase in stiffness. To correctly interpret the DMA results, we developed a new physics-based rheological model for the description of the storage and loss moduli. The model is based on the fractional calculus approach and successfully describes the material rheology in a broad range of temperatures (−70 °C–+70 °C) and frequencies (0.1–100 s−1), using only six physically meaningful fitting parameters for each material. The results provide guidance for the development of nanocomposite PUa-based materials. 

In this work, an open-source computational–statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport is presented. A parallel implementation of the well-known pseudo-spectral method in addition to the comprehensive record of the statistical and small-scale quantities of the turbulent transport are offered for executing on distributed memory CPU-based supercomputers. The user-friendly workflow and easy-to-run design of the developed package are disclosed through an extensive and step-by-step example. The resulting low- and high-order statistical records vividly verify a well-established and fully developed turbulent state as well as the seamless statistical balance of conservation laws. The post-processing tools provided in this platform would allow the user to easily construct multiple important transport quantities from primitive turbulent fields. The programming codes for this tool are accessible through GitHub (see Data Availability Statement). 

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 ana prioriestimate 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-Safaeiet 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. 

We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted for 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 quasi-linear 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 and 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. 

Extensive experimental evidence highlights that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics modeling for scalar turbulence a greater challenge to date. We develop a new large eddy simulation (LES) paradigm for efficiently and dynamically nonlocal LES modeling of the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection–diffusion model, coding the corresponding superdiffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (noninteger) Laplacian exponent, where we, on the fly, calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreement with the ground-truth filtered direct numerical simulation data in comparison to the conventional static and dynamic Prandtl–Smagorinsky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena and, at the same time, providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and very large eddy simulation frameworks even with strong anisotropies, applicable to environmental applications. 

We developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of homogeneous isotropic turbulent flows. The model is based on a generalized (integer-to-noninteger)-order Laplacian of the filtered velocity field, and a novel dynamic model has been formulated to avoid the need for tuning the model constant. Three data-driven approaches were introduced for the determination of the fractional-order to have a model that is totally free of any tuning parameter. Our analysis includes both the a priori and the a posteriori tests. In the former test, using a high-fidelity and well-resolved dataset from direct numerical simulations (DNSs), we computed the correlation coefficients for the stress components of the subgrid-scale (SGS) stress tensor and the one we get directly from the DNS results. Moreover, we compared the probability density function of the ensemble-averaged SGS forces for different filter sizes. In the latter, we employed our new model along with other conventional models including the static and dynamic Smagorinsky models into our pseudo-spectral solver and tested the final predicted quantities. The results of the newly developed model exhibit an expressive agreement with the ground-truth DNS results in all components of the SGS stress and forces. Also, the model exhibits promising results in the VLES region as well as the LES region, which could be remarkably important for cost-efficient nonlocal turbulence modeling, e.g., in meteorological and environmental applications.