A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

A constitutive model for plastically anisotropic solids with non-spherical voids

Plastic constitutive relations are derived for a class of anisotropic porous materials consisting of coaxial spheroidal voids, arbitrarily oriented relative to the embedding orthotropic matrix. The derivations are based on nonlinear homogenization, limit analysis and micromechanics. A variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal spheroidal void and subjected to uniform boundary deformation. To obtain closed form equations for the effective yield locus, approximations are introduced in the limit-analysis based on a restricted set of admissible microscopic velocity fields. Evolution laws are also derived for the microstructure, defined in terms of void volume fraction, aspect ratio and orientation, using material incompressibility and Eshelby-like concentration tensors. The new yield criterion is an extension of the well known isotropic Gurson model. It also extends previous analyses of uncoupled effects of void shape and material anisotropy on the effective plastic behavior of solids containing voids. Preliminary comparisons with finite element calculations of voided cells show that the model captures non-trivial effects of anisotropy heretofore not picked up by void growth models.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

A two-level system with induced transitions as a model of stress relaxation

This paper outlines the basic features of a two-level cooperative model of the stress relaxation in solids. In contrast to similar models presented earlier, the transitions between the two energy levels can take place in both directions, the relaxation process thus assuming a quasi-equilibrium character. The kinetics of this model are the same as obtained in the model where the transitions take place from the higher to the lower level only.Dedicated to Prof. Dr. F. R. Schwarzl on the occasion of his 60th birthday     

A linear complementarity model for multibody systems with frictional unilateral and bilateral constraints

The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions.With the time-stepping impulse-velocity scheme,the measure differential equations are discretized.The equations of horizontal linear complementarity problems(HLCPs),which are used to compute the impulses,are constructed by decomposing the absolute function and the filled-in relay function.These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints,or HLCPs for frictional bilateral constraints.Finally,a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.     

A New dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expessed in terms of not only the dislocation density itself but also their spatial gradients. The linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns. The project supported by the National Natural Science Foundation of China, Grant No.19392300     

A crystal plasticity model for strain-path changes in metals

A model is proposed that deals with the transient mechanical anisotropy during strain-path changes in metals. The basic mechanism is assumed to be latent hardening or softening of the slip systems, dependent on if they are active or passive during deformation, reflecting microstructural mechanisms that depend on the deformation mode rather than on the crystallography. The new model captures the experimentally observed behaviour of cross hardening in agreement with experiments for an AA3103 aluminium alloy. Generic results for strain reversals qualitatively agree with two types of behaviour reported in the literature – with or without a plateau on the stress–strain curve. The influence of the model parameters is studied through detailed calculations of the response of three selected parameter combinations, including the evolution of yield surface sections subsequent to 10% pre-strain. The mathematical complexity is kept to a minimum by avoiding explicit predictions related directly to underpinning microstructural changes. The starting point of the model is a combination of conventional texture and work hardening approaches, where an adapted full-constraints Taylor theory and a simple single-crystal work-hardening model for monotonic strain are used. However, the framework of the model is not restricted to these particular models.     

A model for cell migration in tumour growth

Tumour growth results, in particular, from cell–cell interaction and tumour and healthy cell proliferation. The complexity of the cellular microenvironment may then be framed within the theory of mixtures by looking at cell populations as the constituents of a mixture. In this paper the balance equations are reviewed to account for directionality onto a collective migration of the tumour cell population, via an attractive force of the chemotactic type, in addition to the customary pressure term. The density of tumour cells turns out to be governed by a hyperbolic differential equation. By neglecting, as usual, the inertia term it follows that the density satisfies a backward, or forward, diffusion equation according as the attraction, or pressure effect, prevails. Uniqueness of the solution to the backward equation is investigated and a family of solutions is described. An estimate is given for the growth rate of a tumour profile.     

埋地管道的横向静力分析耦合模型及其解耦条件

现有埋地管道横向静力分析中的刚性管假设可以实现横向分析与纵向分析的解耦,但往往与实际情况不符.为此,本文根据埋地管道的受力特点,建立了考虑纵向内力影响的横向静力分析耦合模型.基于此耦合模型,结合挠曲线方程与纵向内力的关系,推导出横向分析和纵向分析的解耦条件,为建立解耦模型提供了理论基础.与此同时,一方面为便于实用,另一方面为检验解耦模型的误差,文中针对圆环形管道导出了其横截面剪应力分布规律,给出了埋地管道横向静力分析的实用耦合模型,并结合弹性中心法,建议和提出了耦合模型的实现算法.最后,采用耦合模型对两端固定的埋地给水管道进行了横向内力分析及解耦模型的误差探讨.结果表明,管道两端处纵向剪力对横向内力影响显著,解耦模型误差很大;但随着与管端距离的增加纵向剪力的影响急剧减小,近跨中区域解耦误差几乎可忽略不计.     

A reduced-order model manifold technique for automated structural defects judging using the PGD with analytical validation

Automation is conquering new fields on a daily basis. Aiming for faster and more reliable products, industrials as well as researchers are oriented into automation. Non-destructive testing as well as defect quantification is not an exception. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. In this work, we suggest a comprehensive method based on model order reduction techniques to judge if a structure shall be salvaged. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The PGD is a model order reduction technique that allows circumventing the curse of dimensionality by using domain decomposition. Therefore, the 6D simulation illustrated in this paper is performed within a few minutes on a standard laptop. Later on, a stress concentration manifold is built and used online for decision-making. The manifold is validated on a few selected solutions solved analytically using an analytical procedure. The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied.     

A continuum model for initiation and evolution of deformation twinning

Within continuum dislocation theory the plastic deformation of a single crystal with one active slip system under plane-strain constrained shear is investigated. By introducing a twinning shear into the energy of the crystal, we show that in a certain range of straining the formation of deformation twins becomes energetically preferable. An energetic threshold for the onset of twinning is determined. A rough analysis qualitatively describes not only the evolving volume fractions of twins but also their number during straining. Finally, we analyze the evolution of deformation twins and of the dislocation network at non-zero dissipation. We present the corresponding stress-strain hysteresis, the evolution of the plastic distortion, the twin volume fractions and the dislocation densities.     

A model for computational investigation of elasto-plastic normal and tangential contact considering adhesion effect

With the rapid development of Micro-Electro-Mechanical System (MEMS), we enter a field in which the surface effects have dominated many of the micro-scale phenomena, and the adhesive contact is one of the focuses. In this paper, a feasible model for finite element computation is presented via a macroscopic and microscopic combination approach, in which the adhesive forces are simulated by some non-linear spring elements considering the softening stage. Two basic problems concerning the adhesion effect were considered; through specific quantitative analysis, the results show a consistency with the current elastic continuum theories of adhesion and a brief investigation into the effects of adhesion on plastic deformation and tangential contact will be carried out as well. The project supported by the National Natural Science Foundation of China (10172050, 90205022) and Key Grant Project of Chinese MoE (0306)     

A lower bound for a variational model for pattern formation in shape-memory alloys

The Kohn-Müller model for the formation of domain patterns in martensitic shape-memory alloys consists in minimizing the sum of elastic, surface and boundary energy in a simplified scalar setting, with a nonconvex constraint representing the presence of different variants. Precisely, one minimizes

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. The project supported by the National Natural Science Foundation of China (10132020 and 10472027). The English text was polished by Yunming Chen.     

A non-local implicit gradient-enhanced model for unstable behaviors of pseudoelastic shape memory alloys in tensile loading

In this paper, a gradient-enhanced 3-D phenomenological model for shape memory alloys using the non-local theory is developed based on a 1-D constitutive model. The method utilizes a non-local field variable in its constitutive framework with an implicit gradient formulation in order to achieve results independent of the finite element discretization. An efficient numerical approach to implement the non-local gradient-enhanced model in finite element codes is proposed. The model is used to simulate stress drop at the onset of transformation, and its performance is evaluated using different experimental data. The potential of the presented numerical approach for behavior of shape memory alloys in eliminating mesh-dependent simulations is validated by conducting various localization problems. The numerical results show that the developed model can simulate the observed unstable behaviors such as stress drop and deviation of local strain from global strain during nucleation and propagation of martensitic phase.     

A phase field model for failure in interconnect lines due to coupled diffusion mechanisms

We describe a diffuse interface, or phase field model for simulating electromigration and stress-induced void evolution and growth in interconnect lines. Microstructural evolution is tracked by defining an order parameter, which takes on distinct uniform values within solid material and voids, and varying rapidly from one to the other over narrow interfacial layers associated with the void surfaces. The order parameter is governed by a form of the Cahn-Hilliard equation. An asymptotic analysis demonstrates that the zero contour of order parameter tracks the motion of a void evolving by coupled surface and lattice diffusion, driven by stress, electron wind and vacancy concentration gradients. Efficient finite element schemes are described to solve the modified Cahn-Hilliard equation, as well as the equations associated with the accompanying mechanical, electrical and bulk diffusion problems. The accuracy and convergence of the numerical scheme is investigated by comparing results to known analytical solutions. The method is applied to solve various problems involving void growth and evolution in representative interconnect geometries.     

An elasto-plastic constitutive model with plastic strain rate potentials for anisotropic cubic metals

An elasto-plastic constitutive model with the plastic strain rate potential was developed for finite element analysis. In the model, isotropic-kinematic hardening was incorporated under the plane stress condition for anisotropic sheet cubic metal forming analysis. The formulation is general enough for any homogeneous plastic strain rate potential (with the first-order homogeneous effective strain rate) but the plastic strain rate potential Srp2004-18p was considered here. Attention was focused on the development of the elasto-plastic transition criterion and the effective stress update algorithm. Also, to assure the quadratic convergence rate in Newton’s method, the elasto-plastic tangent modulus was analytically derived. Accuracy and convergence of the stress update algorithm were assessed by the iso-error maps, whereas stability of the algorithm was confirmed by analytical procedure. Validations were performed for the examples of the circular cup drawing, 2D draw-bending and unconstrained cylindrical bending tests, utilizing aluminum sheet alloys.     

A fluctuating elastic plate and a cell model for lipid membranes

The thermal fluctuations of lipid bi-layer membranes are key to their interaction with cellular components as well as the measurement of their mechanical properties. Typically, membrane fluctuations are analyzed by decomposing into normal modes or by molecular simulations. Here we propose two new approaches to calculate the partition function of a membrane. In the first approach we view the membrane as a fluctuating von Karman plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and co-variance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute the fluctuations of the membrane of a malaria infected cell and analyze the effects of boundary conditions on fluctuations. Our second approach is based on the cell model of Lennard-Jones and Devonshire. This model, which was developed for liquids, assumes that each molecule fluctuates within a cell on which a potential is imposed by all the surrounding molecules. We adapt the cell model to a lipid membrane by recognizing that it is a 2D liquid with the ability to deform out of plane whose energetic penalty must be factored into the partition function of a cell. We show, once again, that some results on membrane fluctuations can be recovered using this new cell model. However, unlike some well established results, our cell model gives an entropy that scales with the number of molecules in a membrane. Our model makes predictions about the heat capacity of the membrane that can be tested in experiments.