Traditional Continuum Models Research Articles

Development of a Novel Beam-Based Finite-Element Approach for the Computationally Efficient Prediction of Residual Stresses and Displacements in Large 3D-Printed Polymer Parts

Recently, 3D printing of large, structural polymer parts has received increasing interest, especially for the creation of recyclable structural parts and tooling. However, the complexity of large-scale 3D polymeric printing often dictates resource-intensive trial and error processes to achieve acceptable parts. Existing computational models used to assess the impact of fabrication conditions typically treat the 3D-printed part as a continuum, incorporate oversimplified boundary conditions and take hours to days to run, making design space exploration infeasible. The purpose of this study is to create a structural model that is computationally efficient compared with traditional continuum models yet retains sufficient accuracy to enable exploration of the design space and prediction of part residual stresses and deformations. To this end, a beam-based finite element methodology was created where beads are represented as beams, vertical springs represent inter-bead transverse force transfer and multi-point, linear constraints enforce strain compatibility between adjacent beads. To test this framework, the fabrication of a large Polyethylene terephthalate glycol (PETG) wall was simulated. The PETG was modeled as linearly elastic with an experimentally derived temperature-dependent coefficient of thermal expansion and elastic modulus using temperature history imported from an ABAQUS thermal model. The results of the simulation were compared to those from a continuum model with an identical material definition, showing reasonable agreement of stresses and displacements. Further, the beam-based model required an order of magnitude less run time. Subsequently, the beam-based model was extended to allow separation of the part from the printing bed and the inclusion of part self-weight during fabrication to assess the significance of these effects that pose challenges for existing continuum models.

Effective thermo-electric-mechanical modeling of capacitively coupled plasma in low-pressure conditions: Modeling and application in dry etching

In semiconductor dry etching process, capacitively coupled plasma (CCP) is widely used in low-pressure environments. However, the kinetics of species particles in low-pressure conditions are different from the general environments. Traditional continuum models are popular in industry due to their simplicity, but they struggle to account for the kinetics of particles in low-pressure conditions. Although particle-in-cell (PIC) modeling is suitable for simulating the behavior of a single particle, it is difficult to perform such industrial simulations due to the high computational cost. To account for both kinetics and engineering applicability, this study presents an effective thermo-electric-mechanical modeling structure of CCP at low-pressure conditions. This modeling structure includes balance laws of continua derived from the global energy equilibrium containing thermal, electric and mechanical energies. The ion momentum, which is ignored in traditional plasma continuum models, is considered in the balance laws, and electron energy distributions are obtained by solving the Boltzmann equation to obtain the properties of electron transport. In addition, the model variables are calculated based on mixed kinetic theory accounting for the fraction of each species. The results of the proposed modeling are compared to those of a PIC model to validate its ability to describe the distribution of electrons with respect to pressure conditions. Based on the proposed numerical formulations, this study built a MATLAB-based program to guide the design of a screen baffle in dry etching equipment. This program captures the critical aspects of the practical application of screen baffle design in the context of the dry etching process. The results of this paper showed that the proposed model can be applied to engineering applications under low-pressure conditions.

Wetting and non-wetting liquid flow in nanopores: Wettability, non-Poiseuille profile and intermolecular fundamentals

Wetting and non-wetting liquid flow in nanoscale pores or channels is of great interest in many science and technology fields, such as biotechnology, energy storage/conversion and micro-devices. It is also of considerable significance in geosciences and geoengineering. For instance, for the geological disposal of contaminated waste understanding flow and transport in nanoporous rocks is critical for accurately evaluating potential environmental hazards. Similarly, for oil recovery from tight reservoirs, understanding flow mechanisms in nanopores may improve production forecasts and enable the development of strategies to enhance production.This paper presents a comprehensive study on wetting and non-wetting liquid flow in nanopores, including the development of a new nanoflow model and its demonstration using published findings from molecular dynamics simulations and laboratory tests. The new nanoflow model is formulated based on the general two-dimensional Navier-Stokes equations. The novel aspects include: 1) the model incorporates the parameters relating to the intermolecular interactions between the fluid and the solid wall in a nanopore, which are lacking in traditional continuum models; 2) the model contains the effects of wettability and the nanochannel’s dimension on flowrate, which are unique to nanoflows and not considered in traditional continuum models; and 3) the model is based on a two-dimensional non-Poiseuille flow model described by a set of coupled ordinary differential equations. Therefore, the numerical solutions are much easier to obtain than the partial differential equations of non-Poiseuille flow models. The classic Poiseuille flow is its limiting case.Three examples are presented to demonstrate the model’s capability. The first is the determination of the contact angle of water in hydrophobic carbon nanochannels or nanotubes using published results from MD simulations and laboratory tests. The second example uses the new nanoflow model to simulate non-wetting water flow in hydrophobic nanochannels or nanotubes, including flow in a nanoscale graphene slit representative of those present in graphene batteries for energy storage. The results obtained are compared with those obtained from MD simulations. The last example discusses the wetting or partially wetting liquid flow profiles in nanoscale pores. The three examples provide new insights into wetting and non-wetting liquid flow behaviour in nanopores.

Macro autonomous traffic flow model with traffic jerk and downstream vehicle information

PurposeIn the era of connected and autonomous vehicles, a large amount of surrounding vehicular information can be acquired by the focal vehicle in real time using vehicle-to-vehicle communication technology, such as the core variable of electronic throttle opening angle. Meanwhile, the traffic jerk, such as the non-compliance of drivers and pedestrians, worsens the chaos of the surrounding traffic environment. To reflect the future traffic environment, the authors simultaneously incorporate the electronic throttle (ET) and traffic jerk into the traditional continuum model. The authors derive the stability criterion of the enhanced continuum model via the perturbation method.Design/methodology/approachTo facilitate insight into the propagation and evolution mechanism of traffic jam near the stability condition, the authors use the nonlinear stability analysis method to derive the KdV-Burgers equation of proposed continuum model.FindingsThe new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.Originality/valueThe research on autonomous continuum models is rare. This model can better reflect the actual traffic, which can also provide a theoretical reference for the future traffic governance.

Mechanical peeling of van der Waals heterostructures: Theory and simulations

Mechanical peeling is crucial for the assembly process of van der Waals (vdW) heterostructures. We provide a new theory to describe the peeling of vdW heterostructures based on interatomic potential. Representatively, we present the peeling of graphene on molybdenum disulfide (MoS2) using a bottom-up approach. The results show that there are three stages (the initial, stable and jump out of contact stages) in the entire peeling process. We find that the traditional continuum model is only suitable for the stable stage, while our theory can describe the entire process from (the initial unstable) contact to the end of the stable stage. In addition, we discovered a new characteristic length, the elasto-peeling length Lep=2D∕Δγ=4σ02πD∕H, that is a crucial parameter that reflects the bending (D) and interfacial properties (Δγ) of the layered materials during peeling. Finally, the theory as expressed by the Hamaker constant (H) is presented. Our findings may help to reveal the underlying mechanisms in the peeling of layered materials at the atomic scale.

Experimental and Numerical Investigations of Influence on Overland Flow and Water Infiltration by Fracture Networks in Soil

Preferential flow is common in clay or expansive clay soils, involving water bypassing a large portion of the soil matrix. Dye tracer experiment and numerical modeling are used to simulate the surface runoff and subsurface preferential flow patterns influenced by the soil fracture network of a relatively steep hillslope system (slope angle equals to 10 degrees). The result of the experiments indicates that part of the water is infiltrated through cracks, leading to the delay of the initial runoff-yielding time and reduction of the discharge of the surface runoff. The soil water flow is mainly in the matrix when the intensity of precipitation is low. With the increasing of precipitation, soil water movement may become in the form of preferential flow through cracks. In addition, the nonuniformity of soil water infiltration and the depth of the average water infiltration increase as the precipitation intensity increases. To this end, the complete coupling model was established by using the surface-matrix-crack (SMC) model to simulate water flow within discrete fracture as well as to simulate water flow in the soil matrix based on the concept of dual permeability using the traditional Richards’ equation. In this model, the “cubic law” of fluid motion in cracks within smooth parallel plates and the two-dimensional diffusion wave approximation to Saint-Venant equations with momentum term ignored (two-dimensional shallow water equations) were used. The model divides soil water infiltration into two forms and uses the overall method to calculate the exchange of water between the crack networks and matrix regions as well as the exchange water between surface runoff and infiltration water. Results indicate that the SMC model has better performance compared with the traditional equivalent continuum model when those models are used to simulate the surface runoff movement and the soil water movement in the presence of cracks.

Modelling temperature-influenced acidizing process in fractured carbonate rocks

A three-dimensional thermal-hydro-chemical (T-H-C) coupled unified pipe-network method (UPM) is developed to simulate the process of acidizing treatment in fractured carbonate rock. The concept of the traditional two-scale continuum model is extended by considering thermal effects and incorporating multiphysical governing equations for explicitly represented fractures in the current method. An effective conforming mesh method is employed in the element discretizing procedure for the complex fracture network system. Both rock matrix and fractures are modeled by three-dimensional equivalent pipe networks to simulate the H-T-C coupling process in fractured carbonate rock. The fluid transfer between rock matrix and fractures is solved by a superposition principle, without introducing the interchange terms. This straightforward method simplifies the programming process in simulating rock dissolution by acid. The accuracy of the thermal-hydro coupled process is verified against commercial software (COMSOL Multiphysics) result. The reliability of modelling the acidizing process at different temperatures is demonstrated through comparison with previous experimental results. Numerical experiments indicate that the presence of a fracture network, varying reservoir or inlet acid temperature, and formation heterogeneity all influence the acidizing efficiency. The fracture network reduces the volume of acid being injected but has no influence on the dissolution pattern corresponding with specific injection rates. The optimal injection rate increases to from a dominant wormhole in the case with high formation temperature. The acidizing efficiency is reduced when acid with a high temperature is injected. And both optimal injection rate and injection volume increase. For the influence of formation heterogeneity on the dissolving patterns, conical dissolution is observed in comparatively more homogeneous formations with lower porosity heterogeneity. However, ramified dissolution occurs in the extremely heterogeneous formation, and the existence of fracture networks have less influence on the development of wormhole branches. These aforementioned factors should be considered in practical field design to approach optimal acidizing results.

A Cyclical Approach to Continuum Modeling: A Conceptual Model of Diabetic Foot Care.

“Cascade” or “continuum” models have been developed for a number of diseases and conditions. These models define the desired, successive steps in care for that disease or condition and depict the proportion of the population that has completed each step. These models may be used to compare care across subgroups or populations and to identify and evaluate interventions intended to improve outcomes on the population level. Previous cascade or continuum models have been limited by several factors. These models are best suited to processes with stepwise outcomes—such as screening, diagnosis, and treatment—with a single defined outcome (e.g., treatment or cure) for each member of the population. However, continuum modeling is not well developed for complex processes with non-sequential or recurring steps or those without singular outcomes. As shown here using the example of diabetic foot care, the concept of continuum modeling may be re-envisioned with a cyclical approach. Cyclical continuum modeling may permit incorporation of non-sequential and recurring steps into a single continuum, while recognizing the presence of multiple desirable outcomes within the population. Cyclical models may simultaneously represent the distribution of clinical severity and clinical resource use across a population, thereby extending the benefits of traditional continuum models to complex processes for which population-based monitoring is desired. The models may also support communication with other stakeholders in the process of care, including health care providers and patients.

Rational Development of Neutral Aqueous Electrolytes for Zinc-Air Batteries.

Neutral aqueous electrolytes have been shown to extend both the calendar life and cycling stability of secondary zinc–air batteries (ZABs). Despite this promise, there are currently no modeling studies investigating the performance of neutral ZABs. Traditional continuum models are numerically insufficient to simulate the dynamic behavior of these complex systems because of the rapid, orders‐of‐magnitude concentration shifts that occur. In this work, we present a novel framework for modeling the cell‐level performance of pH‐buffered aqueous electrolytes. We apply our model to conduct the first continuum‐scale simulation of secondary ZABs using aqueous ZnCl2–NH4Cl as electrolyte. We first use our model to interpret the results of two recent experimental studies of neutral ZABs, showing that the stability of the pH value is a significant factor in cell performance. We then optimize the composition of the electrolyte and the design of the cell considering factors including pH stability, final discharge product, and overall energy density. Our simulations predict that the effectiveness of the pH buffer is limited by slow mass transport and that chlorine‐containing solids may precipitate in addition to ZnO.

Estimation of fracture distribution in a CO2‐EOR system through Ensemble Kalman filter

AbstractCO2‐EOR can serve as a method to jointly enhance oil production and reduce CO2 emissions into the atmosphere. In a fractured reservoir, it is crucial to characterize the spatial and geometrical properties of fractures when designing a CO2‐enhanced oil recovery (EOR) strategy, since the existence of fractures may lead to the early CO2 breakthrough and can significantly impact the sweep efficiency. Compared with the traditional continuum model, discrete fracture model (DFM) can explicitly maintain the full geometrical properties of the individual fractures and accurately simulate the performance of a CO2‐EOR system. However, the spatial distribution of fractures should be reasonably understood to ensure the effectiveness of CO2‐EOR project. In this work, an approach combining ensemble Kalman filter (EnKF) with DFM is developed to estimate the fracture distribution by matching the history of production data. The spatial distribution of each fracture is characterized by the coordinates of endpoints, length, and orientation. These geometrical properties are treated as the adjustable model parameters during the history matching process. The difficulty to estimate such parameters lies in the non‐linear relationship between parameters and the observed production data. The EnKF method has been found to an effective method to resolve this issue. Here the available production data is assimilated sequentially to update the geometrical parameters of each fracture via the EnKF method, which has the capability to quantify the production dynamics under estimation uncertainty. © 2017 Society of Chemical Industry and John Wiley & Sons, Ltd.

Including surface ligand effects in continuum elastic models of nanocrystal vibrations

The measured low frequency vibrational energies of some quantum dots (QDs) deviate from the predictions of traditional elastic continuum models. Recent experiments have revealed that these deviations can be tuned by changing the ligands that passivate the QD surface. This observation has led to speculation that these deviations are due to a mass-loading effect of the surface ligands. In this article, we address this speculation by formulating a continuum elastic theory that includes the dynamical loading by elastic surface ligands. We demonstrate that this model is capable of accurately reproducing the l = 0 phonon energy across a variety of different QD samples, including cores with different ligand identities and epitaxially grown CdSe/CdS core/shell heterostructures. We highlight that our model performs well even in the small QD regime, where traditional elastic continuum models are especially prone to failure. Furthermore, we show that our model combined with Raman measurements can be used to infer the elastic properties of surface bound ligands, such as sound velocities and elastic moduli, that are otherwise challenging to measure.

Theoretical study of the spectroscopic and nonlinear optical properties of trans- and cis-4-hydroxyazobenzene.

We investigate the molecular structure, vibrational and electronic absorption spectra, and electronic hyperpolarizabilities of trans and cis isomers of 4-hydroxyazobenzene (HOAB) via density functional theory. Results show that the azo dye exhibits a high third-order nonlinear optical response and good optical transparency. Both the basis set and the functional are important influences on the results obtained when calculating the absorption spectrum and NLO response. We also study the effect of the solvent on the electronic absorption spectrum to assess the ability of the functional to reproduce the experimental spectrum in combination with a suitable solvent model. Our calculations show that the SMD model of Truhlar et al. handles the electrostatic and the non-electrostatic effects of hydrogen-bonding solvents on the absorption spectrum better than the traditional polarizable continuum model does. In addition, our results indicate that the dye trans-HOAB exhibits a high second hyperpolarizability and excellent optical transparency. Also, although the second hyperpolarizability of cis-HOAB is much lower than that of trans-HOAB, it is non-negligible when calculating the optical nonlinearity of HOAB under an optical pump. We also examine the effect of frequency dispersion on second harmonic generation. This study provides the basis for further research on the spectroscopic and nonlinear optical properties of novel azo dyes and other π-conjugated compounds.

Meso‐scale statistical properties of gas–solid flow—a direct numerical simulation (DNS) study

Statistical properties of particles in heterogeneous gas–solid flow were numerically investigated based on the results of a three‐dimensional large‐scale direct numerical simulation (DNS). Strong scale‐dependence and local non‐equilibrium of these properties, especially the particle fluctuating velocity (PFV) or granular temperature, were observed to be related to the effect of meso‐scale structures formed by the compromise in competition between fluid and particle dominated mechanisms. To quantify such effects, the heterogeneous structures were partitioned into a gas‐rich dilute phase and a solid‐rich dense phase according to the particle‐scale voidage defined through the Voronoi tessellation. Non‐equilibrium features, such as the deviation of PFV from Gaussian distribution and anisotropy, were found even in phase‐specific properties. A new distribution function for the PFV well characterizing these features was obtained by fitting the DNS results, which takes a typical bi‐disperse mode, with phase‐specific granular temperatures. The implications of these findings to the kinetic theory of granular flow and traditional continuum models of gas–solid flow were also discussed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3–14, 2017

A meshfree method for bending and failure in non-ordinary peridynamic shells

The peridynamic theory of solid mechanics offers an integral based alternative to traditional continuum models based on partial differential equations. This formulation is particularly advantageous when applied to material failure problems that result in discontinuous displacement fields. This paper presents a meshfree implementation of a state-based peridynamic bending model based on the idea of rotational springs between pairs of peridynamic bonds. Energy-based analysis determines the properties of these bond pairs for a brittle material, resulting in a constitutive model that naturally gives rise to localized damage and crack propagation.

Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems

The use of rigorous verification methods is a powerful tool which permits progress in the analysis of dynamical processes that is not possible using purely analytical techniques. In this paper we develop a set of tools for branch validation, which allows for the rigorous verification of branch behavior, bifurcation, and solution index on branches generated through a saddle-node bifurcation. While the presented methodology can be applied in a variety of settings, we illustrate the use of these tools in the context of materials science. In particular, lattice models have been proposed as a more realistic reflection of the behavior of materials than traditional continuum models. For example, unlike their continuum counterparts, lattice models can account for phenomena such as pinning, and a significant body of work has been developed to study traveling waves. However, in a variety of other contexts such as bifurcation theory, questions about lattice dynamical systems are significantly harder to answer than t...

A lattice Boltzmann model for heat and mass transfer phenomena with phase transformations in unsaturated soil during freezing process

In this paper, a mesoscopic numerical model for simulating the heat and moisture transport phenomena in frozen soil during freezing process is presented. The model includes a stochastic generation-growth method for reconstructing the soil structure with given macroscopic geometric parameters, a lattice Boltzmann method (LBM) model for solving multiphase fluid flow and a LBM model for solving heat conduction with phase change in porous media. By using the present model, freezing process in sandy loam soil is demonstrated. Two types of boundary condition, prescribed temperature and adiabatic boundary conditions are employed in the given cases. All the numerical results show good agreement with experimental results. Considering the mesoscopic nature of LBM, the proposed model is a potential alternative to traditional continuum models.

Optimization Design of Single Track Railway Tunnel Lining Structure

Based on the traditional safety coefficient method,Continuum Model and single track railway tunnel lining structure, the paper does numerical simulation calculates and compares effects of actions on tunnel lining structure, analyses and get the effect of actions in different section of tunnel lining.According to the tunnel lining element’s safety coefficient and standard requirements, reasonable lining structure thickness is gave by comparison and optimization of lining structure thickness,and this provides the theory support for the structure design of track railway tunnel .

A particle based simulation model for glacier dynamics

Abstract. A particle-based computer simulation model was developed for investigating the dynamics of glaciers. In the model, large ice bodies are made of discrete elastic particles which are bound together by massless elastic beams. These beams can break, which induces brittle behaviour. At loads below fracture, beams may also break and reform with small probabilities to incorporate slowly deforming viscous behaviour in the model. This model has the advantage that it can simulate important physical processes such as ice calving and fracturing in a more realistic way than traditional continuum models. For benchmarking purposes the deformation of an ice block on a slip-free surface was compared to that of a similar block simulated with a Finite Element full-Stokes continuum model. Two simulations were performed: (1) calving of an ice block partially supported in water, similar to a grounded marine glacier terminus, and (2) fracturing of an ice block on an inclined plane of varying basal friction, which could represent transition to fast flow or surging. Despite several approximations, including restriction to two-dimensions and simplified water-ice interaction, the model was able to reproduce the size distributions of the debris observed in calving, which may be approximated by universal scaling laws. On a moderate slope, a large ice block was stable and quiescent as long as there was enough of friction against the substrate. For a critical length of frictional contact, global sliding began, and the model block disintegrated in a manner suggestive of a surging glacier. In this case the fragment size distribution produced was typical of a grinding process.

First Principles Simulations of Nanoscale Silicon Devices With Uniaxial Strain

We report parameter-free first principle atomistic simulations of quantum transport in Si nanochannels under uniaxial strain. Our model is based on the density functional theory (DFT) analysis within the Keldysh nonequilibrium Green's function (NEGF) formalism. By employing a recently proposed semi-local exchange along with the coherent potential approximation we investigate the transport properties of two-terminal Si nanodevices composed of large number of atoms and atomic dopants. Simulations of the two-terminal device based on the NEGF-DFT are compared quantitatively with the traditional continuum model to establish an important accuracy benchmark. For bulk Si crystals, we calculated the effects of uniaxial strain on band edges and effective masses. For two-terminal Si nanochannels with their channel length of ~ 10 nm, we study the effects of uniaxial strain on the electron transport. With 0.5% uniaxial tensile strain, the conductance along [110] direction is increased by ~ 8% and that along [001] is increased by ~ 2%, which are comparable with the other reported results. This paper qualitatively and quantitatively shows the current capability of first principle atomistic simulations of nanoscale semiconductor devices.

An implicit lattice Boltzmann model for heat conduction with phase change

In this work, a new variation of the lattice Boltzmann method (LBM) was developed to solve the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term was treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The Bhatnagar–Gross–Krook (BGK) approximation with a D2Q9 lattice was applied and different boundary conditions including Dirichlet and Neumann boundary conditions were considered. The developed model was tested by solving a one-dimensional melting problem for a pure metal, and one and two-dimensional solidification problems for a binary alloy. The results of the LBM solution were compared with analytical and finite element solutions and a good consistency was observed. Considering the special capabilities that LBM offers, like local characteristic, and inherent parallel structure, the developed model is an interesting alternative to traditional continuum models.