Finite deformation continuum model for single-walled carbon nanotubes

A continuum-based model for computing strain energies and estimating Young’s modulus of single-walled carbon nanotubes (SWCNTs) is developed by using an energy equivalence-based multi-scale approach. A SWCNT is viewed as a continuum hollow cylinder formed by rolling up a flat graphite sheet that is treated as an isotropic continuum plate. Kinematic analysis is performed on the continuum level, with the Hencky (true) strain and the Cauchy (true) stress being employed to account for finite deformations. Based on the equivalence of the strain energy and the molecular potential energy, a formula for calculating Young’s modulus of SWCNTs is derived. This formula, containing both the molecular and continuum scale parameters, directly links macroscopic responses of nanotubes to their molecular structures. Sample numerical results show that the predictions by the new model compare favorably with those by several existing continuum and molecular dynamics models.     

A multi-scale simulation of tungsten film delamination from silicon substrate

To bridge the different spatial scales involved in the process of tungsten (W) film delaminating from silicon (Si) substrate, a multi-scale simulation procedure is proposed via a sequential approach. In the proposed procedure, a bifurcation-based decohesion model, which represents the link between molecular and continuum scales, is first formulated within the framework of continuum mechanics. Molecular dynamics (MD) simulation of a single crystal W block under tension is conducted to investigate the effect of specimen size and loading rate on the material properties. The proposed decohesion model is then calibrated by using MD simulation of a single crystal W block under tension and using available experimental data, with a power scaling law to account for the size effect. A multi-scale model-based simulation of W film delamination from Si substrate is performed by using the proposed procedure within the framework of the material point method. The simulated results provide new insights into the mechanisms of the film delamination process.     

Computation of head–disk interface gap micro flowfields using DSMC and continuum–atomistic hybrid methods

This paper discusses computational modeling of micro flow in the head–disk interface (HDI) gap using the direct simulation Monte Carlo (DSMC) method. Modeling considerations are discussed in detail both for a stand‐alone DSMC computation and for the case of a hybrid continuum–atomistic simulation that couples the Navier–Stokes (NS) equation to a DSMC solver. The impact of the number of particles and number of cells on the accuracy of a DSMC simulation of the HDI gap is investigated both for two‐ and three‐dimensional configurations. An appropriate implicit boundary treatment method for modeling inflow and outflow boundaries is used in this work for a three‐dimensional DSMC micro flow simulation. As the flow outside the slider is in the continuum regime, a hybrid continuum–atomistic method based on the Schwarz alternating method is used to couple the DSMC model in the slider bearing region to the flow outside the slider modeled by NS equation. Schwarz coupling is done in two dimensions by taking overlap regions along two directions and the Chapman–Enskog distribution is employed for imposing the boundary condition from the continuum region to the DSMC region. Converged hybrid flow solutions are obtained in about five iterations and the hybrid DSMC–NS solutions show good agreement with the exact solutions in the entire domain considered. An investigation on the impact of the size of the overlap region on the convergence behavior of the Schwarz method indicates that the hybrid coupling by the Schwarz method is weakly dependent on the size of the overlap region. However, the use of a finite overlap region will facilitate the exchange of boundary conditions as the hybrid solution has been found to diverge in the absence of an overlap region for coupling the two models. Copyright © 2009 John Wiley & Sons, Ltd.     

Non-periodic finite-element formulation of orbital-free density functional theory

We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real-space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.     

钢-混凝土混合框架结构多尺度分析及其建模方法

多尺度计算是保证计算精度的同时最大限度降低计算代价的有效途径,在众多学科领域和工程问题中都得到了应用.在结构有限元多尺度分析领域,要解决的一个关键问题是如何实现局部微观模型与宏观结构模型之间的共同工作.为实现精细有限元模型在植入宏观结构模型时不同尺度模型界面的变形协调,提出有限元微观模型与宏观模型的界面连接方法,给出了轴向、横向和转角的约束方程.通过编制用户子程序,使该方法在有限元软件中得以实现,并通过简单的圆柱筒算例,对界面连接的合理性进行了验证.最后基于多尺度建模方法和复杂混合结构节点的精细模型,给出了钢-混凝土混合框架结构多尺度弹塑性时程分析的应用实例,结果表明多尺度计算可较好模拟节点的复杂边界条件.本文建议的界面连接方法可有效实现不同尺度模型界面的变形协调,为工程结构进行多尺度提供了条件.     

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综述了连续介质方法在碳纳米管研究中的最新进展. 主要叙述梁、壳模型, 膜模型,多尺度方法,分子结构力学方法,非局部连续介质方法,以及无网格法的基本原理、 基本方法,及其最新进展,指出其局限性,并预测连续介质方法在碳纳米管研究的发展趋势 和方向.     

Transient stress wave propagation in one-dimensional micropolar bodies

Certain types of structures and materials, such as engineered multi-scale systems and comminuted zones in failed ceramics, may be modeled using continuum theories incorporating additional kinematic degrees of freedom beyond the scope of classical continuum theories. If such material systems are to be subjected to high strain rate loads, such as those resulting from ballistic impact or blast, it will be necessary to develop models capable of describing transient stress wave propagation through these media. Such a model is formulated, solved, and applied to the impact between two bodies and to a two-layer bar or strip subjected to an instantaneously applied stress. Results from these examples suggest that the model parameters, and therefore constitutive properties and geometries, may be tuned to reduce and control the transmission of stress through these bodies.     

Modeling of properties and motions of an inhomogeneous one-dimensional continuum of a complicated Cosserat-type microstructure

We consider an approach to modeling the properties of the one-dimensional Cosserat continuum [1] by using the mechanical modeling method proposed by Il’yushin in [2] and applied in [3]. In this method, elements (blocks, cells) of special form are used to develop a discrete model of the structure so that the average properties of the model reproduced the properties of the continuum under study. The rigged rod model, which is an elastic structure in the form of a thin rod with massive inclusions (pulleys) fixed by elastic hinges on its elastic line and connected by elastic belt transmissions, is taken to be the original discrete model of the Cosserat continuum. The complete system of equations describing the mechanical properties and the dynamical equilibrium of the rigged rod in arbitrary plane motions is derived. These equations are averaged in the case of a sufficiently smooth variation in the parameters of motion along the rod (the long-wave approximation). It was found that the average equations exactly coincide with the equations for the one-dimensional Cosserat medium [1] and, in some specific cases, with the classical equations of motion of an elastic rod [4–6]. We study the plane motions of the one-dimensional continuum model thus constructed. The equations characterizing the continuum properties and motions are linearized by using several assumptions that the kinematic parameters are small. We solve the problem of natural vibrations with homogeneous boundary conditions and establish that each value of the parameter distinguishing the natural vibration modes is associated with exactly two distinct vibration mode shapes (in the same mode), each of which has its own frequency value.     

COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1 ) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow,and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

An atomistic–continuum hybrid scheme for numerical simulation of droplet spreading on a solid surface

We present an atomistic–continuum hybrid method to investigate spreading dynamics of drops on solid surfaces. The Navier–Stokes equations are solved by the finite-volume method in a continuum domain comprised of the main body of the drop, and atomistic molecular dynamics simulations are used in a particle domain in the vicinity of the contact line. The spatial coupling between the continuum and particle domains is achieved through constrained dynamics of flux continuities in an overlap domain.     

多尺度复合材料力学研究进展

多尺度复合材料力学是运用多尺度分析思想研究空间分布非均匀材料力学性能的学科, 近年来,多 组分、多层级先进材料的蓬勃发展和微纳米实验观测手段的不断进步,有力地推动了该学科的研究,论文围绕非均 匀材料力学性能的多尺度分析,首先从微纳米尺度到宏观尺度综述了常用的理论分析方法;接着分别针对非均匀 连续介质和离散体系介绍了常用的多尺度计算模拟方法;然后结合本课题组在纳米复合材料、抗冲击吸能材料、随 机网络材料和多层级自相似材料等方面的研究工作,举例说明了如何综合运用多种方法对各种复杂材料系统进行 多尺度分析;最后,展望了该领域还需进一步发展和完善的若干方向。     

Non-classic modeling of three-dimensional manipulation with different geometry of atomic force microscopy components: Multi-scale approach

The size effect must be considered for dynamic modeling of an AFM since the dimensions of the AFM, are in micro-scale. In this study, a three-dimensional multi-scale method based on a non-classical continuum mechanic theory is developed in order to include material length scale parameter (MLSP) in the dynamic behavior of manipulation carried out by AFM. First, the governing equations of Macro Field (MF) are derived using the modified coupled stress theory and the Kirchhoff plate model. Moreover, Nano Field (NF) is modeled using the molecular dynamics equations. The MF and the NF are then combined employing the multi-scale algorithm. Rectangular and dagger cantilevers are taken into account to obtain manipulation results. The influence of two types of tip on the manipulation results is also investigated. The obtained results show that the deformations of the AFM components in non-classic models are less than the one in the classical model. Furthermore, Root Mean Square (RMS) results for a nano-particle demonstrates that damage and deformation of the nano-particle are underestimated by the classical model. The investigations carried out in the present study show the significance of employing the non-classical theory for analyzing AFM performance, particularly for estimation of separation time span.     

Magnetooptical, electrooptical and photoelastic effects in an elastic polarizable and magnetizable isotropic continuum

The magnetooptical, electrooptical and photoelastic behaviour of an elastic polarizable and magnetizable isotropic continuum are investigated from a dynamical point of view, starting from balance equations and constitutive relations. The most original result of the theory is the fact that the continuum exhibits the Cotton-Mouton effect, together with linear birefringence of transverse sound waves. This is compared with experimental data and quantum theory results.As expected, the continuum does not exhibit Faraday rotation.     

Phase boundary motion in an elastic bar of finite length

Using the continuum mechanical model of solid-solid phase transitions of Abeyaratne and Knowles, this paper examines the large time dynamical behavior of a phase boundary. The problem studied concerns a finite elastic bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. Interaction between the moving phase boundary and the elastic waves generated by an impact at the end of the bar and subsequent reflections is studied in detail by using a finite difference scheme. The numerical results show that the phase boundary in a finite bar returns to an equilibrium state after a disturbance of finite duration, whether the two-phase material is trilinear or not.     

DSMC／EPSM混合算法研究

将EPSM算法与DSMC方法结合，构造了可模拟含近连续流区及过渡流区的DSMC/EPSM混合算法。运用混合算法模拟了马赫数等于5时超音速竖板绕流及马赫数等于4时超音速平板绕流，并将结果与DSMC算法的结果进行比较，证明了DSMC／EPSM混合算法的有效性，同时将EPSM算法与DSMC算法的效率进行了比较。     

大型射电望远镜悬挂馈源舱-Stewart 平台系统耦合分析

针对大射电望远镜悬挂系统特殊的结构形式,采用分离舱索系统和Stewart平台,应用有限元和牛顿-欧拉方程混合方法,提出Stewart平台与悬索馈源舱系统的混合动力学耦合方程,在此基础上,应用最优控制理论,通过Ham ilton-Jacobi-Isaacs不等式,探讨了耦合方程的解耦问题,得出在一定条件下具有鲁棒性的Stewart平台所允许的最大质量。数值仿真验证了方法的有效性和合理性。     

Numerical Simulation of Nanoindentation and Patch Clamp Experiments on Mechanosensitive Channels of Large Conductance in <Emphasis Type="Italic">Escherichia coli</Emphasis>

A hierarchical simulation framework that integrates information from all-atom simulations into a finite element model at the continuum level is established to study the mechanical response of a mechanosensitive channel of large conductance (MscL) in bacteria Escherichia coli (E. coli) embedded in a vesicle formed by the dipalmitoylphosphatidycholine (DPPC) lipid bilayer. Sufficient structural details of the protein are built into the continuum model, with key parameters and material properties derived from molecular mechanics simulations. The multi-scale framework is used to analyze the gating of MscL when the lipid vesicle is subjective to nanoindentation and patch clamp experiments, and the detailed structural transitions of the protein are obtained explicitly as a function of external load; it is currently impossible to derive such information based solely on all-atom simulations. The gating pathways of E. coli-MscL qualitatively agree with results from previous patch clamp experiments. The gating mechanisms under complex indentation-induced deformation are also predicted. This versatile hierarchical multi-scale framework may be further extended to study the mechanical behaviors of cells and biomolecules, as well as to guide and stimulate biomechanics experiments.     

The Nonlinear Heat Equation on W-Random Graphs

For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medvedev (The nonlinear heat equation on dense graphs and graph limits. ArXiv e-prints, 2013) justify the continuum (thermodynamic) limit for a large class of coupled dynamical systems on convergent families of graphs.     

Bifurcation of elastic tank-liquid coupled sloshing system

The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established. By means of the multi-scale method and the singularity theory, the bifurcation behaviors of the system are investigated and analyzed. The various nonlinear dynamical behaviors of the coupling system are obtained, which can further explain the relationship between the physical parameters and the bifurcation solutions. The results provide a theoretical basis to the realization of the parameter optimal control.