Continuum Model Research Articles

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow.

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF's unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately . We then use the theoretical model to predict VWF's behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately , matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

Insight on relationship between crystallinity and band gap energies of polyhydroxyalkanoates polymers

This study explores the electronic properties of polyhydroxyalkanoates (PHAs), a class of biodegradable polymers. The focus lies in examining the relationship between crystallinity and band gap energies in PHAs. A notable discovery is the identification of a band gap plateau, suggesting a threshold in electronic properties with increasing polymer chain length. DFT calculations were employed to model the complexities of PHA polymers, with the conductor-like polarizable continuum model (CPCM) offering insights into solvent effects. The results demonstrate a strong negative correlation between crystallinity and band gap in both vacuum and CPCM environments. This study underscores the significance of structural order in shaping the electronic properties of PHAs, paving the way for the development of sustainable polymeric materials for various applications.

Johnson–Cook yield functions for cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) derived from single crystal plasticity models

High-fidelity constitutive models are critical for accurate meso-scale continuum modeling and prediction of shock initiation of crystalline energetic materials (EMs). While empirically calibrated or atomistic-guided anisotropic elastoplastic models of EM such as cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) capture important micromechanical phenomena (such as dislocation evolution, slip-resistance, and anisotropic elasticity), the computational cost of using anisotropic single-crystal plasticity models can become prohibitive for meso-scale computations of void-collapse and hotspot formation in microstructures. Thermo-mechanically representative, isotropic, pressure, temperature, and rate-dependent material constitutive models are practical alternatives for meso-scale simulations of the shock response of microstructures. To this end, this work constructs physically consistent isotropic plasticity from anisotropic single-crystal plasticity models for HMX and RDX. State-of-the-art crystal plasticity models for HMX and RDX are used to compute the stress states in single crystals oriented in three different directions relative to shocks generated by impact at velocities ranging from 100 to 1000 m/s. Post-shock von Mises stress fields for the three orientations are then used to calibrate the strain-rate hardening coefficient and the reference strain rate for a rate-dependent Johnson–Cook (JC) yield surface model. We compare the pressures and the post-shock von Mises stresses between the JC and the anisotropic models to show that the isotropic computations closely approximate the averaged deformation response of the three different crystal orientations. We then model the interaction of a shock generated by a 500 m/s impact with a 0.5 μm void and show that the pressures and the deviatoric stresses obtained using the isotropic model closely match those computed from anisotropic models for both HMX and RDX. The resulting isotropic J2 plastic flow model for HMX and RDX can be employed to perform meso-scale simulations for energy localization due to shear bands and void collapse in the two materials.

Elastic particle model for coil-stretch transition of dilute polymers in an elongational flow

The phenomenon of the ‘coil-stretch’ (C-S) transition, wherein a long-chain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviours under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf (J. Chem. Phys., vol. 20, 1952, pp. 395–402), we introduce a continuum model in this study to investigate the C-S transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strain-hardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steady-state deformation using a polarization method. By employing this reduced model, we effectively capture the C-S transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a force-balance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. We demonstrate that our model, while simple, unveils rich elastohydrodynamics of the C-S transition.

Equivalent micropolar model for porous guided bone regeneration mesh: Optimum design for desired mechanical properties

In the present work, a micropolar continuum model is adopted to homogenise a heterogeneous porous model of Guided Bone Regeneration (GBR) meshes. GBR meshes are used in dentistry as mechanical barriers to isolate and protect the area of bone loss from the surrounding tissue while allowing new bone growth. The mechanical constants of the continuum are derived based on the strain energy equivalence of a periodic porous plate with its equivalent ortho-tetragonal micropolar model under prescribed boundary conditions. The effects of various architectural features such as pore shapes, patterns and sizes on the material parameters are investigated. The results show that the micropolar theory provides a better prediction of the response of the 2D porous geometries considered for the GBR mesh, compared to the classical Cauchy theory. The collected equivalent material parameters are further used for GBR mesh design, considering both mechanical and biomedical requirements. As an example, different materials and arrangements are analysed to find micropolar constitutive parameters that are comparable to bone parameters reported in the literature. This allows the GBR mesh to possess the mechanical performance that matches the adjacent bones.

Effects of gas velocity on nonequilibrium characteristics of fluidization

The gas velocity is a key factor of the macroscale operating conditions, affecting the nonequilibrium behavior and regime transitions of fluidization, but the mechanism of its effects remains unclear, resulting in a deterioration of the accuracy of the two-fluid model (TFM) simulation with the increase of the gas velocity. To seek its underlying mechanism, we performed time-resolved, particle-tracking velocimetry (PTV) measurements of a fluidized bed operated under bubbling to turbulent states, thereon the analysis of the probability density distribution of particle velocity, and hydrodynamic parameters. It is found that a stronger nonequilibrium exists with the increase of the gas velocity, in the sense that the bimodal distribution of particle velocity is more significant at turbulent fluidization. The total fluctuating energy and stress show a scale separation, suggesting that a reasonable continuum modeling should take into account the whole range of fluctuation.

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration.

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1's contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration.

Molecular Simulations Reveal the Free Energy Landscape and Transition State of Membrane Electroporation.

The formation of pores over lipid membranes by the application of electric fields, termed membrane electroporation, is widely used in biotechnology and medicine to deliver drugs, vaccines, or genes into living cells. Continuum models for describing the free energy landscape of membrane electroporation were proposed decades ago, but they have never been tested against spatially detailed atomistic models. Using molecular dynamics (MD) simulations with a recently proposed reaction coordinate, we computed potentials of mean force of pore nucleation and pore expansion in lipid membranes at various transmembrane potentials. Whereas the free energies of pore expansion are compatible with previous continuum models, the experimentally important free energy barrier of pore nucleation is at variance with established models. The discrepancy originates from different geometries of the transition state; previous continuum models assumed the presence of a membrane-spanning defect throughout the process, whereas, according to the MD simulations, the transition state of pore nucleation is typically passed before a transmembrane defect has formed. A modified continuum model is presented that qualitatively agrees with the MD simulations. Using kinetics of pore opening together with transition state theory, our free energies of pore nucleation are in excellent agreement with previous experimental data.

Identifying Second-Gradient Continuum Models in Particle-Based Materials with Pairwise Interactions Using Acoustic Tensor Methodology

Identifying Second-Gradient Continuum Models in Particle-Based Materials with Pairwise Interactions Using Acoustic Tensor Methodology

A computational approach to identify the material parameters of the relaxed micromorphic model

We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squares fitting of the total energy of the relaxed micromorphic homogeneous continuum to the total energy of the fully-resolved heterogeneous microstructure, governed by classical linear elasticity. We avoid establishing exact micro–macro transition relations, as in classical homogenization theory, because defining a representative volume element is not feasible in the absence of scale separation, as such an element does not exist. The relaxed micromorphic model is a generalized continuum that utilizes the Curl of a micro-distortion field instead of its full gradient as in the classical micromorphic theory, leading to several advantages and differences. The most crucial advantage is that it operates between two well-defined scales. These scales are determined by linear elasticity with microscopic and macroscopic elasticity tensors, which respectively bound the stiffness of the relaxed micromorphic continuum from above and below. While the macroscopic elasticity tensor is established a priori through standard periodic first-order homogenization, the microscopic elasticity tensor remains to be determined. Additionally, the characteristic length parameter, associated with curvature measurement, controls the transition between the micro- and macro-scales. Both the microscopic elasticity tensor and the characteristic length parameter are here determined using a computational approach based on the least squares fitting of energies. This process involves the consideration of an adequate number of quadratic deformation modes and different specimen sizes. We conduct a comparative analysis between the least square fitting results of the relaxed micromorphic model, the fitting of a skew-symmetric micro-distortion field (Cosserat-micropolar model), and the fitting of the classical micromorphic model with two different formulations for the curvature; one simplified formulation involving only one single characteristic length and a simplified isotropic curvature with three parameters. The relaxed micromorphic model demonstrates good agreement with the fully-resolved heterogeneous solution after optimizing only four parameters. The “simplified” full micromorphic model, which includes isotropic curvature and involves the optimization of seven parameters, does not achieve superior results, while the Cosserat model exhibits the poorest fitting.

CMC/SWCNT biocomposites: A combined study on experiments, molecular simulations and continuum models

A comprehensive study is carried out including experimental, molecular dynamics (MD) simulations and continuum modelling of Carboxymethyl cellulose/Single walled carbon nanotube (CMC/SWCNT) biocomposites. The electrical, optical, and mechanical properties of CMC/SWCNT biocomposites were investigated in the experimental part of this work. In the result of measurements, it was determined that electrical conductivity (σdc), absorbance level (A) and tensile modulus (E) of the composites increased significantly with the increase of SWCNT content in the CMC matrix. These physical changes in the CMC/SWCNT composites were explained by the percolation theory and the electrical and optical percolation thresholds (Rσ and Rop) and the critical exponents (βσ and βop) of these composites were calculated. In addition, MD simulations were performed to estimate the material properties for the polymer composite structures. The results of the tensile test experiments were found to qualitatively overlap with the experiments at low concentration range. Moreover, a homogenous distribution of SWCNTs were observed in the CMC matrix together with a strong level of interactions in between. In the continuum modelling a two parameters augmentation model is used. A coupled Mori-Tanaka-self consistent method is utilized when obtaining effective properties of composites. Experimental, MD and continuum modelling results of composites were compared and reasonable agreement was obtained between results.

Prediction of direct shear failure in blast-loaded reinforced concrete members

The occurrence of direct shear failure in structural members during the early phases of blast loading prior to the development of appreciable curvature can lead to sudden and catastrophic consequences for protected facilities exposed to near-field and/or close-in blasts. Thus, accurately predicting direct shear failure in structural members subjected to blast loads is crucial. Consequently, this paper presents a novel 3-D finite element (FE)-based cohesive interface modeling approach capable of capturing the shear slip near the supports and accurately predicting direct shear failure in blast-loaded reinforced concrete (RC) members. The validity of the proposed numerical model is established with experimental data. Three distinct blast load cases varying from distant to close-in are applied to verify the applicability and highlight the novelty of the proposed model. Results show that direct shear failure is inherently captured within the modeling framework of the proposed cohesive interface models, eliminating the need for externally adopted damage criteria seen in existing 3-D FE-based continuum models. Further, the effectiveness of the cohesive interface model in the accurate blast damage assessment of structural members is manifested by using pressure-impulse (P-I) diagrams.

Concise Spectrotemporal Studies of Magnetar SGR J1935+2154 Bursts

SGR J1935+2154 has truly been the most prolific magnetar over the last decade: it has been entering into burst active episodes once every 1–2 yr since its discovery in 2014, it emitted the first Galactic fast radio burst associated with an X-ray burst in 2020, and it has emitted hundreds of energetic short bursts. Here, we present the time-resolved spectral analysis of 51 bright bursts from SGR J1935+2154. Unlike conventional time-resolved X-ray spectroscopic studies in the literature, we follow a two-step approach to probe true spectral evolution. For each burst, we first extract spectral information from overlapping time segments, fit them with three continuum models, and employ a machine-learning-based clustering algorithm to identify time segments that provide the largest spectral variations during each burst. We then extract spectra from those nonoverlapping (clustered) time segments and fit them again with the three models: the cutoff power-law model, the sum of two blackbody functions, and the model considering the emission of a modified blackbody undergoing resonant cyclotron scattering, which is applied systematically at this scale for the first time. Our novel technique allowed us to establish the genuine spectral evolution of magnetar bursts. We discuss the implications of our results and compare their collective behavior with the average burst properties of other magnetars.

Optimization of Active Chlorine Production in a Filter-Press Type Electrochemical Reactor through Continuum Modelling and Response Surface Methodology

This study proposes a methodology to optimize the design of an electrochemical flow-by reactor to increase the active chlorine production. The performances of various reactor configurations were evaluated using Computational Fluid Dynamics, starting from the dimensions of the well-known FM01-LC reactor channel (B = 4 cm, L = 16 cm, and S = 1 cm), increasing or decreasing each component by 25%. These conditions were calculated using a Box-Behnken design of experiments, screening out the above dimensions as parameters in addition to the volumetric flow, which was operated at two different rates: 1 and 5 l min−1. A surface response methodology (RSM) was utilized to optimize the response variables, and determine the best design parameters. The combined computational study herein proposed suggests that the optimization of the flow electrochemical reactor design is a compromise between the flow uniform distribution, and mass transfer. It is found that the optimization method used is adequate at the experimental level, since the optimized channel (0.01 M) presents better performance than the conventional FM01-LC channel (0.002 M), after 60 min of experimental electrolysis. It is expected the current analysis will contribute to the development of new filter-press-type electrochemical reactors optimizing chlorine production for numerous applications.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses: discrete and continuum models

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses: discrete and continuum models

Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme

AbstractStrain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained.

The Initial Conditions of Clustered Core Collapse: Multiwavelength Analysis of Oph A SM1N and N6 at 100 au Resolution

We present new Atacama Large Millimeter/submillimeter Array (ALMA) continuum and NH2D, N2D+, and H2D+ line emission at matched, ∼100 au resolution toward the dense star-forming cores SM1N and N6 within the Ophiuchus molecular cloud. We determine the density and temperature structure of SM1N based on radiative transfer modeling and simulated observations of the multiwavelength continuum emission at 0.8, 2, and 3 mm. We show that SM1N is best fit by either a broken power-law or Plummer-like density profile with high central densities (n ∼ 108 cm−3), and an inner transition radius of only ∼80–300 au. The free-fall time of the inner region is only a few ×103 yr. The continuum modeling rules out the presence of an embedded first hydrostatic core (FHSC) or protostar. SM1N is therefore a dynamically unstable but still starless core. We find that NH2D is likely depleted at high densities within SM1N. The nonthermal velocity dispersions increase from NH2D to N2H+ and H2D+, possibly tracing increasing (but still subsonic) infall speeds at higher densities as predicted by some models of starless core contraction. Toward N6, we confirm the previous ALMA detection of a faint, embedded point source (N6-mm) in 0.8 mm continuum emission. NH2D and N2D+ avoid N6-mm within ∼100 au, while H2D+ is not strongly detected toward N6. The distribution of these tracers is consistent with heating by a young, warm object. N6-mm thus remains one of the best candidate FHSCs detected so far, although its observed (sub)millimeter luminosity remains below predictions for FHSCs.

Accuracy of ALMA estimates of young disk radii and masses

Context. Protoplanetary disks, which are the natural consequence of the gravitational collapse of the dense molecular cloud cores, host the formation of the known planetary systems in our universe. Substantial efforts have been dedicated to investigating the properties of these disks in the more mature Class II stage, either via numerical simulations of disk evolution from a limited range of initial conditions or observations of their dust continuum and line emission from specific molecular tracers. The results coming from these two standpoints have been used to draw comparisons. However, few studies have investigated the main limitations at work when measuring the embedded Class 0/I disk properties from observations, especially in a statistical fashion. Aims. In this study, we provide a first attempt to compare the accuracy of some critical disk parameters in Class 0/I systems, as derived on real ALMA observational data, with the corresponding physical parameters that can be directly defined by theoreticians and modellers in numerical simulations. The approach we follow here is to provide full post-processing of the numerical simulations and apply it to the synthetic observations the same techniques used by observers to derive the physical parameters. Methods. We performed 3D Monte Carlo radiative transfer and mock interferometric observations of the disk populations formed in a magnetohydrodynamic (MHD) simulation model of disk formation through the collapse of massive clumps with the tools RADMC-3D and CASA, respectively, to obtain their synthetic observations. With these observations, we re-employed the techniques commonly used in disk modelling from their continuum emissions to infer the properties that would most likely be obtained with real interferometers. We then demonstrated how these properties may vary with respect to the gas kinematics analyses and dust continuum modelling. Results. Our modelling procedure, based on a two-component model for the disk and the envelope, shows that the disk sizes can be properly recovered from observations with sufficient angular resolutions, with an uncertainty of a factor ≈1.6–2.2, whereas their masses cannot be accurately measured. Overall, the masses are predominantly underestimated for larger, more massive disks by a median factor of ≈2.5, and even up to 10 in extreme cases, with the conversion from flux to dust mass under the optically thin assumption. We also find that the single Gaussian fittings are not a reliable modelling technique for young, embedded disks characterised by a strong presence of the envelopes. Thus, such an approach is to be used with caution. Conclusions. The radiative transfer post-processing and synthetic observations of MHD simulations offer genuine help in linking important observable properties of young planet-forming disks to their intrinsic values in simulations. Further extended investigations that tackle the caveats of this study, such as the lack of variation in the dust composition and distribution, dust-to-gas ratio, and other shortcomings in the numerical models, would be essential for setting constraints on our understanding of disk and planet formations.

A data-driven multiscale model for reactive wetting simulations

We describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

Comparison of finite element modeling approaches for Ti6Al4V porous bone implants

Additive technologies have made it possible to make a significant breakthrough in the development and production of personalized porous implants, which have clear advantages over monolithic predecessors. At the same time, engineers are faced with a number of new tasks, one of which is correct and effective numerical modeling of porous implants in the process of solving optimization problems. The study compares approaches to numerical modeling of porous titanium for bone implants, taking into account differences in the mechanical parameters of the material and the geometry of the models. The detailed geometry of the structure of 9 models is considered, for which two variants of material parameters are specified: pure Ti6Al4V alloy and experimental ones obtained for specimens printed from Ti6Al4V powder. As a proposed approach to homogenizing the structure, a continuum model of a cylinder is considered, for which the experimental properties of the specimen’s material are specified. The numerically obtained values of Young's moduli for each approach are compared with those obtained in the experiment. It has been established that when setting the properties of a pure alloy, the calculated Young's modulus exceeds the experimental one by 83–92 %. The closest thing to experiment is detailed modeling of geometry with setting the experimental properties of the material structure, while the calculated Young's modulus does not exceed the experimental one by more than 10 %. However, in this case the calculation takes from 2 to 8 hours. In the case of continuum modeling, the calculated Young's moduli exceed the calculated moduli in detailed modeling by no more than 11 %, while the calculation lasts no more than 1 minute. Based on this, it is proposed to use a continuum approach to modeling implants in the process of calculating the optimization of their shape, as an initial iteration before detailed modeling of the structure. As material properties, it is necessary to use the mechanical parameters of the structures, previously obtained from uniaxial compression experiments. Using the properties of a pure alloy will lead to results that significantly exceed the actual ones when calculating the porous structure.