A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

A multiscale model was proposed to calculate the circumferential stress （CS） and wall shear stress （WSS） and analyze the effects of global and local factors on the CS, WSS and their synergy on the arterial endothelium in large straight arteries. A parameter pair [Zs, SPA] （defined as the ratio of CS amplitude to WSS amplitude and the phase angle between CS and WSS for different harmonic components, respectively） was proposed to characterize the synergy of CS and WSS. The results demonstrated that the CS or WSS in the large straight arteries is determined by the global factors, i.e. the preloads and the afterloads, and the local factors, i.e. the local mechanical properties and the zero-stress states of arterial walls, whereas the Zs and SPA are primarily determined by the local factors and the afterloads. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and the stress phase difference SPA might be appropriate indices to reflect the influences of the states of whole downstream arterial beds on the local blood flow-dependent phenomena such as angiogenesis, vascular remodeling and atherosgenesis.

Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales.The present work develops a multiscale model by coupling the volume of fluid(VOF)method and a discrete bubble model(DBM),to simulate the cavitating flow in a convergent-divergent test section.The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure,and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles.An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation.For the flow field,the very large eddy simulation(VLES)approach is applied.Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted.Compared with the experimental observations,it is shown that the cavitation inception,bubble clouds formation and glass cavity generation are all well represented,indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.

A Multiscale Model of Mass-Functionally Graded Beam-Fluid System Under Bending and Vibration Responses

In this paper,a multiscale model is developed for the mass functionally graded(FG)beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests,which are determined by two aspects.At the microstructural level,the gradient variation is realized by arbitrary distribution of matrix pores,and the effective moduli under specific distribution are obtained using the micromechanics homogenization theory.In the meantime,at the structural level,the mechanical responses of FG porous beams subjected to mass loading are considered in a static fluid environment.Then,the explicit expressions of local finite-element(FE)expressions corresponding to the static and dynamic responses are given in the appendices.The present results are validated against numerical and experimental results from the literature and mechanical tests of 3D printed structures,with good agreement generally obtained,giving credence to the present model.On this basis,a comprehensive parametric study is carried out,with a particular focus on the effects of boundary conditions,fluid density,and slenderness ratio on the bending and vibration of FG beams with several different gradations.

Multiscale tensegrity model for the tensile properties of DNA nanotubes

DNA nanotubes(DNTs)with user-defined shapes and functionalities have potential applications in many fields.So far,compared with numerous experimental studies,there have been only a handful of models on the mechanical properties of such DNTs.This paper aims at presenting a multiscale model to quantify the correlations among the pre-tension states,tensile properties,encapsulation structures of DNTs,and the surrounding factors.First,by combining a statistical worm-like-chain(WLC)model of single DNA deformation and Parsegian's mesoscopic model of DNA liquid crystal free energy,a multiscale tensegrity model is established,and the pre-tension state of DNTs is characterized theoretically for the first time.Then,by using the minimum potential energy principle,the force-extension curve and tensile rigidity of pre-tension DNTs are predicted.Finally,the effects of the encapsulation structure and surrounding factors on the tensile properties of DNTs are studied.The predictions for the tensile behaviors of DNTs can not only reproduce the existing experimental results,but also reveal that the competition of DNA intrachain and interchain interactions in the encapsulation structures determines the pre-tension states of DNTs and their tensile properties.The changes in the pre-tension states and environmental factors make the monotonic or non-monotonic changes in the tensile properties of DNTs under longitudinal loads.

A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY

Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.

Multiscale modeling of mechanical behavior and failure mechanism of 3D angle-interlock woven aluminum composites subjected to warp/weft directional tension loading

The mechanical behavior and progressive damage mechanism of novel aluminum matrix composites reinforced with 3D angle-interlock woven carbon fibers were investigated using a multiscale modeling approach.The mechanical properties and failure of yarns were evaluated using a microscale model under different loading scenarios.On this basis,a mesoscale model was developed to analyze the tensile behavior and failure mechanism of the composites.The interfacial decohesion,matrix damage,and failure of fibers and yarns were incorporated into the microscopic and mesoscopic models.The stress–strain curves and fracture modes from simulation show good agreement with the experimental curves and fracture morphology.Local interface and matrix damage initiate first under warp directional tension.Thereafter,interfacial failure,weft yarn cracking,and matrix failure occur successively.Axial fracture of warp yarn,which displays a quasi-ductile fracture characteristic,dominates the ultimate composites failure.Under weft directional tension,interfacial failure and warp yarn rupture occur at the early and middle stages.Matrix failure and weft yarn fracture emerge simultaneously at the final stage,leading to the cata-strophic failure of composites.The weft directional strength and fracture strain are lower than the warp directional ones because of the lower weft density and the more serious brittle fracture of weft yarns.

Multiscale model of micro curing residual stress evolution in carbon fiber-reinforced thermoset polymer composites

In this study,the micro curing residual stresses of carbon fiber-reinforced thermoset polymer(CFRP)composites are evaluated using a multiscale modeling method.A thermochemical coupling model is developed at the macroscale level to obtain the distributions of temperature and degree of cure.Meanwhile,a representative volume element model of the composites is established at the microscale level.By introducing the information from the macroscale perspective,the curing residual stresses are calculated using the microscale model.The evolution of curing residual stresses reveals the interaction mechanism of fiber,matrix,and interphase period during the curing process.Results show that the curing residual stresses mostly present a tensile state in the matrix and a compressive state in the fiber.Furthermore,the curing residual stresses at different locations in the composites are calculated and discussed.Simulation results provide an important guideline for the analysis and design of CFRP composite structures.

Dynamic Elastic Modulus of Cement Paste at Early Age based on Nondestructive Test and Multiscale Prediction Model

This paper introduced a nondestructive testing method to evaluate the dynamic elastic modulus of cement paste. Moreover, the effect of water-cement ratio and conventional admixtures on the dynamic elastic modulus of cement paste was investigated, in which three kinds of admixtures were taken into account including viscosity modifying admixture （VMA）, silica.fume （SF）, and shrinkage-reducing admixture （SRA）. The experimental results indicate that the dynamic elastic modulus of cement paste increases with decreasing water-cement ratio. The addition of SF increases the dynamic elastic modulus, however, the overdosage of VMA causes its reduction. SRA reduces the dynamic elastic modulus at early age without affecting it in later period. Finally, a multiscale micromechanics approach coupled with a hydration model CEMHYD3D and percolation theory is utilized to predict the elastic modulus of cement paste, and the predictive results by the model are in accordance with the experimental data.

A micro–macro constitutive model for rock considering breakage effects

The paper proposes a three-scale binary medium-based constitutive model on the basis of the meso structures and micro components to describe the elasto-plastic mechanical behavior of mudstone samples.Based on the breakage mechanism of geomaterials,mudstone samples are considered as two different materials(bonded and frictional elements)at mesoscales.From micro to meso scales,given the similar but different mineralogy composition and porosity of the bonded and frictional elements at microscale,as well as their separate mechanical characteristics,different homogenization methods are adopted to obtain their respective meso mechanical properties.At the mesoscale,in view of the unique meso structures and the continuous material transformation,the extended self-consistent scheme(SCS)is improved to be adaptable to elasto-plastic composites with varying meso components.With the consideration of the evolution form of the breakage ratio under the external loading being given based on the assumed strength distribution of the meso bonded elements,the mechanical relations between meso and macro scales are established.Finally,on the basis of the mean-field method and combined with the critical mechanical connections between different scales,the micro-meso-macro constitutive model for mudstone samples are proposed.The model validation shows that,with a few model parameters,the proposed model can well reflect the stress and deformation features of mudstone samples with complex micro-components.

Multiscale modeling of the atmospheric environment over a forest canopy

Vegetation constitutes one of the fundamental types of land use on Earth.The presence of trees in urban areas can decrease local winds and exchange sensible and latent heat with the surrounding environments,thus exerting notable influences on the urban microenvironment.A better understanding of the turbulent transfer of momentum and scalars around vegetation canopy could significantly contribute to improvement of the urban environment.This work develops a large-eddy simulation(LES)method that is applicable to model the flow and scalar transport over the forest canopy.We study the atmospheric flow over complex forested areas under typical weather conditions by coupling LES to the mesoscale model.Models of radiation and energy balance have been developed with explicit treatment of the vegetation canopy.By examining the flow over a forest canopy under a range of stability conditions,we found that buoyancy enhances or suppresses turbulent mixing in unstable or stable atmosphere respectively,with decreasing or increasing wind shear,respectively.From the multiscale modeling of the Beijing Olympic Forest Park,the present coupling scheme proves to better resolve the diurnal variations in wind speed,temperature,and relative humidity over complex urban terrains.The coupling scheme is superior to the traditional mesoscale model in terms of wind field simulation.This is mainly because the coupling scheme not only takes the influences of external mesoscale flow into consideration,but also resolves the heterogeneous urban surface at a fine scale by downscaling,thus better reproducing the complex flow and turbulent transport in the urban roughness sublayer.

Method of cells-based multiscale modeling of elastic properties of filament wound C/C-SiC including free Si and matrix porosity

Three different multiscale models, based on the method of cells(generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent modeling of all phases using the generalized method of cells, synergistic(two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical(one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC.Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute. Finally, un-reacted Si(or free Si) and porosity in the C matrix are included in the multiscale model, and the effect of these new phases on the stiffness and local stresses are considered.

A Gaussian process regression accelerated multiscale model for conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties

Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal properties complicates the problem. In this work, a multiscale model is proposed for the conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties. Homogenization analysis of the coupled conduction and radiative transfer equations is conducted, in which the temperature dependence of thermal properties is considered. Both the macroscopic homogenized equations and the local unit cell problems are derived. It is proved that the macroscopic average temperature can be used in the unit cell problems for the first-order corrections of the temperature and radiative intensity, and the calculations of effective thermal properties. The temperature dependence of thermal properties only influences the higher-order corrections. A multiscale numerical method is proposed based on the analysis. The Gaussian process (GP) regression is coupled into the multiscale algorithm to build a correlation between thermal properties and temperature for the macroscale iterations and prevent the repetitive solving of unit cell problems. The GP model is updated by additional solutions of unit cell problems during the iteration according to a variance threshold. Numerical simulations of conduction-radiation heat transfer in composite with isotropic and anisotropic periodic structures are used to validate the proposed multiscale model. It is found that the accuracy and efficiency of the multiscale method can be guaranteed by using a proper variance threshold for the GP model. The multiscale model can provide both the average temperature and radiative intensity fields and their detailed fluctuations due to the local structures.

Compositional colored Petri net approach to multiscale modeling for systems biology

Colored Petri nets have been demonstrated as a powerful tool for modeling multiscale systems biology.However,the construction of colored Petri nets for biological systems requires prior knowledge about colored Petri nets and is often error-prone and cum-bersome for biologists,especially when the communication between components and hierarchical organization of components in a multiscale model are an issue.To address this problem,an established way is to develop small components and then compose them into bigger models.In this paper,we present a compositional colored Petri net approach to aid automatic modeling of systems biology,and demonstrate it with two case stud-ies.We focus on the modeling of communication between components and hierarchical organization of components as they are key to build multiscale models.

A primer on multiscale modelling of infectious disease systems

The development of multiscale models of infectious disease systems is a scientific endeavour whose progress depends on advances on three main frontiers:(a)the conceptual framework frontier,(b)the mathematical technology or technical frontier,and(c)the scientific applications frontier.The objective of this primer is to introduce foundational concepts in multiscale modelling of infectious disease systems focused on these three main frontiers.On the conceptual framework frontier we propose a three-level hierarchical framework as a foundational idea which enables the discussion of the structure of multiscale models of infectious disease systems in a general way.On the scientific applications frontier we suggest ways in which the different structures of multiscale models can serve as infrastructure to provide new knowledge on the control,elimination and even eradication of infectious disease systems,while on the mathematical technology or technical frontier we present some challenges that modelers face in developing appropriate multiscale models of infectious disease systems.We anticipate that the foundational concepts presented in this primer will be central in articulating an integrated and more refined disease control theory based on multiscale modelling-the all-encompassing quantitative representation of an infectious disease system.

Sequential Multiscale Modeling Using Sparse Representation

The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent variables.The constitutive relation of a polymeric fluid is a function of six variables,even after making the simplifying assumption that stress depends only on the rate of strain.Precomputing such a function is usually considered too expensive.Consequently the value of sequential multiscale modeling is often limited to“parameter passing”.Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables.This strategy dramatically increases the efficiency of sequential multiscale modeling,making it very competitive in many situations.

Modified micro-mechanics based multiscale model for progressive failure prediction of 2D twill woven composites

To consider fiber random distribution at the microscale for the multiscale model based on the micro-mechanics failure(MMF)theory,clustering method is used for the extraction of amplification factors.As the clustering method is a kind of unsupervised machine learning method,the elements with similar mechanical behavior under external loading can be included in a cluster automatically at the microscale.With this modification,the fiber random distribution model can be used for multiscale damage analysis in the framework of MMF theory.To validate the modified multiscale analysis method,progressive damage analysis of a kind of 2D twill woven composites is conducted based on different microscale models.The stress values for microscale models with fiber hexagonal and random distribution patterns are compared first.Much higher stress concentration is generated in the fiber random distribution model due to the smaller inter-fiber distance especially under longitudinal shear loading.The obtained cluster distribution results exhibit the characters of the stress distribution in the two microscale models.Thereafter,tensile and compressive responses of the 2D twill woven composite are predicted with the modified multiscale analysis method and accuracy of the method is verified through comparison with published experimental results.From the simulation results,it can be found that the matrix damage initiation from the model based on the fiber random distribution model is premature compared with that from the model based on the fiber hexagonal distribution model.Besides,under tensile loading,the damage all initiates from the fill tows and propagates to the wrap tows.However,under compressive loading,the matrix damage initiates from the wrap tows in the model based on the fiber random distribution model.

Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.

Multiscale Mechanics and Optimization of Gastropod Shells

A vast majority of mollusks grow a hard shell for protection. The structure of these shells comprises several levels of hierarchy that increase their strength and their resistance to natural threats. This article focuses on nacreous shells, which are composed of two distinct layers. The outer layer is made of calcite, which is a hard but brittle material, and the inner layer is made of nacre, a tough and ductile material. The inner and outer layers are therefore made of materials with distinct structures and properties. In this article, we demonstrate that this system is optimum to defeat attacks from predators. A two-scale mod- eling and optimization approach was used. At the macroscale, a two-layer finite element model of a seashell was developed to capture shell geometry. At the microscale, a representative volume element of the microstructure of nacre was used to model the elastic modulus of nacre as well as a multiaxial failure criterion, both expressed as function of microstructural parameters. Experiments were also performed on actual shells of red abalone to validate the results obtained from simulations and gain insight into the way the shell fails under sharp perforation. Both optimization and experimental results revealed that the shell displays optimum performance when two modes of failure coincide within the structure. Finally, guidelines for designing two-layer shells were proposed to improve the performance of engineered protective systems undergoing similar structural and loading conditions.

Numerical Modelling of the Powder Metallurgical Manufacturing Chain of High Strength Sintered Gears

This paper presents a digital model for the powder metallurgical(PM)production chain of high-performance sintered gears based on an integrated computational materials engineering(ICME)platform.Discrete and finite element methods(DEM and FEM)were combined to describe the macroscopic material response to the thermomechanical loads and process conditions during the entire production process.The microstructural evolution during the sintering process was predicted on the meso-scale using a Monte-Carlo Model.The effective elastic properties were determined by a homogenization method based on modelling a representative volume element(RVE).The results were subsequently used for the FE modelling of the heat treatment process.Through the development of multi-scale models,it was possible obtain characteristics of the microstructural features.The predicted hardness and residual stress distributions allowed the calculation of the tooth root load bearing capacity of the heat-treated sintered gears.

Discontinuous-Galerkin-Based Analysis of Traffic Flow Model Connected with Multi-Agent Traffic Model

As the number of automobiles continues to increase year after year,the associated problem of traffic congestion has become a serious societal issue.Initiatives to mitigate this problem have considered methods for optimizing traffic volumes in wide-area road networks,and traffic-flow simulation has become a focus of interest as a technique for advance characterization of such strategies.Classes of models commonly used for traffic-flow simulations include microscopic models based on discrete vehicle representations,macroscopic models that describe entire traffic-flow systems in terms of average vehicle densities and velocities,and mesoscopic models and hybrid(or multiscale)models incorporating both microscopic and macroscopic features.Because traffic-flow simulations are designed to model traffic systems under a variety of conditions,their underlyingmodelsmust be capable of rapidly capturing the consequences of minor variations in operating environments.In other words,the computation speed of macroscopic models and the precise representation of microscopic models are needed simultaneously.Thus,in this study we propose a multiscale model that combines a microscopic model—for detailed analysis of subregions containing traffic congestion bottlenecks or other localized phenomena of interest-with a macroscopic model enabling simulation of wide target areas at a modest computational cost.In addition,to ensure analytical stability with robustness in the presence of discontinuities,we discretize our macroscopic model using a discontinuous Galerkin finite element method(DGFEM),while to conjoin microscopic and macroscopic models,we use a generating/absorbing sponge layer,a technique widely used for numerical analysis of long-wavelength phenomena in shallow water,to enable traffic-flow simulations with stable input and output regions.