用于C-C共价键力能关系表征的等效C-C键合单元

基于Born-Oppenheimer近似的二次函数形式的势能关系,研究了C-C键沿键轴伸缩、在σ平面和π平面内旋转的力学表征.在原子的平衡位置附近和线弹性的范围内,得到了基于原子核位移表达的平衡关系.在定义一个C-C共价键上两个原子的6个位移自由度的基础上,构建了完整的等效C-C键合单元.当对构成晶形碳的C-C共价键的六环结构进行建模时,等效C-C键合单元方法能够反映出共价键中的键长、键角和键能这三大特征.通过对石墨片和C60分子振动的计算分析和实验比较,得到等效C-C键单元中的力常数,并讨论了力常数的变化状况.该文还对单壁碳纳米管的拉伸弹性模量进行了计算分析,取得较好的效果.等效C-C键合单元可以为碳材料的大规模分子力学计算提供一种实用方法.     

纳米级石墨晶体层片力学性能的等效模型及分析

石墨晶体是由碳原子以sp2杂化轨道和邻近的三个碳原子形成共价键,在其平面内再构成网状层片结构。文中对基于原子键合力能关系的CCBE等效模型和经典的BEAM单元等效模型作了比较分析。其中CCBE包括两个节点,每个节点包含三个平移自由度。与经典BEAM单元相比,其两个节点均没有转动自由度。CCBE和BEAM单元的各个参数可以通过石墨晶体的相关实验获得。通过对石墨晶体层片的拉伸、剪切等效模型的柔度(刚度)系数计算分析,并与实验数据相对比,验证了CCBE等效建模方法的正确性和合理性。该等效建模方法为研究石墨的微观结构、性能等提供了一种有效的数值模拟方法。     

碳纳米管的等价柔性节点空间框架模型

小变形情况下,碳纳米管C-C共价键间的相互作用可以用基于分子力学的宏观力学模型进行模拟.其中,基于分子结构力学的等价结构力学模型是最为有效的碳纳米管弹性参数的预测模型.现有的碳纳米管的等价结构力学模型是用具有刚性节点的空间框架结构模拟碳纳米管的原子晶格受力和变形的关系.根据碳纳米管的原子晶格的变形特点,本文首次提出了一个用柔性节点空间框架模拟碳纳米管原子晶格键角变化的分析模型,再通过应变能等价推导了柔性节点的等价抗弯刚度与分子力学中力常数的关系,从而给出了一个更精确的计算碳纳米管等价弹性参数的分子结构力学模型.文中用ANSYS计算了不同尺寸的锯齿型(zigzag)和扶手型(armchair)单壁碳纳米管的轴向杨氏模量、泊松比、剪切模量及径向杨氏模量,分析了碳纳米管的尺寸效应,并且与其它各种模型所得结果进行了比较.计算结果表明,本文所给碳纳米管的等价柔性节点空间框架模型不仅计算简单、高效,而且准确;并可以直接推广到多壁碳纳米管等价弹性模量的计算及碳纳米管的稳定和动力分析.     

考虑碳纳米管非均匀分布的复合材料电导率计算

碳纳米管作为导电相在机敏复合材料中广泛应用,但碳纳米管为团簇材料,在基体中很难均匀分散。本文考虑碳纳米管的非均匀分布特性,提出了计算碳纳米管复合材料电导率的数值方法。通过引入随机谐和函数,建立了碳纳米管体积分数的三维随机场模型。基于细观力学的有效介质理论、Mori-Tanaka方法和H-S界限理论,考虑碳纳米管之间的隧穿效应,发展了复合材料微小体积单元的电导率计算方法。在此基础上,构建了考虑碳纳米管非均匀分布的复合材料等效电导率三维有限元计算模型。数值分析结果与试验值能够很好吻合,表明这一方法可以准确计算碳纳米管复合材料的电导率。本文进一步分析了碳纳米管非均匀分布对复合材料电导率的影响。     

基于多层模拟方法的双层梁断裂有限元分析

本文提出一种用于含分层的双层梁线弹性断裂分析的有限元方法．将上下子梁均模拟为多个子层,采用只有平动位移自由度的新型梁单元,假设单元内的位移沿纵向和横向均线性变化,推导了该单元的单元刚度矩阵．将开裂部分和未开裂部分的子梁进行单元刚度矩阵组装,施加相应的等效结点力,得到整体平衡方程,并结合边界条件进行求解．为验证该方法的有效性和精度,开展非对称双悬臂梁(Asymmetric Double Cantilever Beam, ADCB)和单臂弯曲梁(Single Leg Bending, SLB)试样的断裂分析,利用虚拟裂纹闭合技术(Virtual Crack Closure Technique, VCCT)得到了试样的能量释放率及其分量,并将求得的结果与解析解和二维有限元解进行对比．计算结果表明,相对于传统双层模拟方法,该多层模拟方法能够精确、高效地计算各类梁试样的能量释放率及其分量,并且无需引入界面连续条件．     

基于高阶Cauchy-Born准则的单壁碳纳米管本构模型

提出了一种基于高阶Cauchy—Born准则建立单壁碳纳米管本构模型的方法。通过引入高阶变形梯度,合理地修正了传统Cauchy—Born准则在描述纳米管变形几何关系时所存在的缺陷。利用原子间相互作用势以及能量等效原理,得到了基于广义连续介质模型的单壁碳纳米管的本构关系。由此得到的本构参数不仅与变形梯度张量F,而且与其梯度F相关,因此是一种广义连续介质模型。利用这样的本构模型,本文还对单壁碳纳米管的杨氏模量进行了预测,并与采用其他方法得到的结果进行了对比,从而证实了所提出方法的有效性。     

一类多孔固体的等效偶应力动力学梁模型

一维多孔固体结构可采用等效连续介质梁模型来研究其动力学行为. 当类梁结构的高度尺寸和多孔固体单胞结构尺寸相近时,等效模型的力学行为会产生尺寸效应现象. 等效经典模型由于不包含尺度参数而无法描述尺寸相关特点,而广义连续介质力学模型则可以准确地考虑尺寸效应的影响. 基于偶应力理论,对一类单胞含有圆形孔洞的周期性多孔固体类梁结构,给出了分析其横向自由振动的等效连续介质铁木辛柯梁模型. 通过对单胞分析,在应变能等价和几何平均的意义下,定义了等效偶应力介质的材料常数. 利用已有的材料常数,推导了等效铁木辛柯梁的动力学微分方程. 将实际多孔固体结构进行完全的动力学有限元离散计算,所获得的解作为精确解以检验等效梁模型所获得的频率和振型的精度. 振型的比较借助于模态置信准则矩阵方法. 大量算例表明,等效偶应力铁木辛柯梁模型在频率和振型两方面均具有较高的计算精度. 重点研究了单胞孔径的相对大小、类梁结构高度与单胞尺寸比以及类梁结构长高比对等效梁模型精度的影响. 在此基础上,偏保守地建议了多孔固体类梁结构自振分析方法.      

三角形截面梁柱构件的三维等效弹簧计算模型

传统有限元在分析梁柱构件时一般采用常应变单元和双线性单元,但此类单元在梁柱构件受弯分析中计算精度不是很高.本文根据梁柱构件的力学性能,在三维连续介质体受到轴向变形和弯曲变形的状态下,利用其轴向变形和弯曲挠度相同,得到具有相同宽度和高度且刚度等效的超静定桁架力学模型.然后,通过桁架杆的截面参数求得弹簧的刚度系数,从而得等效弹簧元模型.本文提出的等效弹簧模型计算方法简单,便于扩展到更为复杂的构件分析中.     

大型渡槽动力建模研究

根据渡槽系薄壁杆件结构的特点,提出了渡槽薄壁结构空间动力分析模型。采用空间梁段单元进行离散,考虑渡槽横向、竖向、纵向、自由扭转和约束扭转变形,由能量原理推导给出了渡槽槽身结构的单元刚度矩阵、质量矩阵的显示表达式;渡槽支架采用空间梁单元模拟;渡槽支架与槽身联贯的盆式橡胶支认采用弹性元件单元模拟。文中具体计算了某大型渡槽的模态,计算结果表明：该模型计算渡槽结构的固有频率与理论解和用大型结构分析程序SAP计算的结果良好接近。本文模型计算简单,使用方便,是大型渡槽动力分析的实用模型。     

含芯拧绞绳非线性弯曲动力学特性分析与研究

建立细长缆索大柔性多体动力学模型时,现实存在的复杂捻制几何构型多不予考虑,而是将柔索简化为材料均匀梁进行描述,致使运动仿真模型与物理实际存在一定差距. 为此,研究一种典型非线性拧绞绳股的大变形等效动力学建模方法,考虑准静态与大范围运动情况下绳股内的线接触,计算了受摩擦力及弯曲曲率影响的绳股可变弯曲刚度,通过等效梁模型避免了绳股精细建模时的大规模计算消耗. 基于连续介质力学与绝对节点坐标方法,建立了拧绞绳惯性广义坐标下的多柔体动力学模型. 为了验证等效模型的可行性,与基于有限段方法建立的精细模型进行对比仿真分析,通过位形验证了等效模型的精度. 进一步地,根据力载作用下的准静态构型,研究了特定构型绳股弯曲刚度沿轴向的分布规律;通过自重力下一端固定柔性绳摆自由运动仿真并与传统均匀梁模型相比,研究了模型弯曲特性的差异. 最后,根据能量守恒原理分析了摩擦耗散系统内各种能量间的相互转化. 拧绞绳大变形等效动力学模型能够提高绳索动力系统运动预测的仿真计算效率,还能为钢丝绳参数与构型设计提供依据.      

A modified Stillinger–Weber potential-based hyperelastic constitutive model for nonlinear elasticity

The Stillinger–Weber (SW) potential, which is a combination of the two- and three-body interaction, states that the bond energy is not only related to the distance between atoms, but also related to the bond angles subtended by this given bond and other bonds. The bond energy mechanism presented by the SW potential is different from that by the classical potentials, such as the Lennard–Jones, Tersoff and Embedded Atom potentials. Different micro energy mechanism reveals different micro fracture mechanism. The original SW potential takes the ‘ideal’ tetrahedral angle as the reference value of each bond angle in the current configuration, which makes it only applicable to the silicon materials. However, the micro fracture mechanism revealed by the SW potential should not be confined to the silicon materials. To extend the SW potential to a wider range of materials, the value of the bond angle in the reference configuration, not the ‘ideal’ tetrahedral angle, is taken as the reference value of this bond angle in the current configuration. Based on this modified SW potential, a constitutive model is developed. By this way, the micro fracture mechanism invoked by the SW potential is incorporated into the constitutive relation. Through this proposed constitutive model, it is found that the Hookean matrix derived from the SW potential matches that of a linear elastic continuum, which suggests that there exists a corresponding relationship between the micro physical parameters of SW potential and the macro material constants. The corresponding micro–macro parameter relationship is derived in this paper. To examine the application of this method to other materials, it is used to simulate the mixed fracture growth in concrete under static and dynamic load. The simulation results suggest that the present method can capture the characters of fracture growth in the quasi-brittle materials. It suggests that the constitutive model based on the modified SW potential can be applied to materials other than silicon. Because the interatomic potential-incorporated constitutive model makes the fracture criterion as the intrinsic property of a constitutive relation, it presents many advantages in fracture simulation. This paper enriches the constitutive relation with the micro fracture mechanism presented in SW potential, providing a new micro constitutive model for materials. Besides this, it also provides a feasible approach to calibrating the parameters of the SW potential for a certain material.     

Ultrasonic beam steering using Neumann boundary condition in multiplysics

The traditional one-dimensional ultrasonic beam steering has time delay and is thus a complicated problem. A numerical model of ultrasonic beam steering using Neumann boundary condition in multiplysics is presented in the present paper. This model is based on the discrete wave number method that has been proved theoretically to satisfy the continuous conditions. The propagating angle of novel model is a function of the distance instead of the time domain. The propagating wave fronts at desired angles are simulated with the single line sources for plane wave. The result indicates that any beam angle can be steered by discrete line elements resources without any time delay.     

A structural mechanics approach for predicting the mechanical properties of carbon nanotubes

Based on molecular mechanics, a structural mechanics model of carbon nanotubes (CNTs) was developed with special consideration given to the bending stiffness of the graphite layer. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds in a CNT. In contrast to the original model developed by Li and Chou (Int. J. Solids Struct. 40(10):2487–2499, 2003), in the current model the out-of-plane deformation (inversion) of the bond was distinguished from the in-plane deformation by considering a rectangular cross-section for the beam element. Consequently, the model is able to study problems where the effect of local bending of the graphite layer in a carbon nanotube is significant. A closed-form solution of the sectional properties of the beam element was derived analytically. The model was verified through the analysis of rolling a graphite sheet into a carbon nanotube. Using the present model, the buckling behavior of nanotubes under bending is simulated. The predicted critical bending angle agrees well with molecular dynamics simulations.     

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. Prom 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.     

Discrete Homogenization in Graphene Sheet Modeling

Graphene sheets can be considered as lattices consisting of atoms and of interatomic bonds. Their bond lengths are smaller than one nanometer. Simple models describe their behavior by an energy that takes into account both the interatomic lengths and the angles between bonds. We make use of their periodic structure and we construct an equivalent macroscopic model by means of a discrete homogenization technique. Large three-dimensional deformations of graphene sheets are thus governed by a membrane model whose constitutive law is implicit. By linearizing around a prestressed configuration, we obtain linear membrane models that are valid for small displacements and whose constitutive laws are explicit. When restricting to two-dimensional deformations, we can linearize around a rest configuration and we provide explicit macroscopical mechanical constants expressed in terms of the interatomic tension and bending stiffnesses.     

A 2-D lattice model for simulating the failure of paper

A new two-dimensional network model is proposed as a micromechanics model to simulate paper’s failure process due to sequentially breakages of fibers and/or bonds. Paper is approximated as a network composed of fibers any two of which link to each other by their intersecting point, namely so-called bond. Fibers distribute along three particular directions, leading to network’s macro-level isotropy. In the framework of finite element method, nodes correspond to fiber-to-fiber bonds, while elements are fiber segments between every two neighboring nodes and described by Timoshenko beam theory. Element breaks when its equivalent internal tensile stress reaches the tensile strength of fiber. Strength of nodes, i.e. fiber-to-fiber bonds is assumed to be dependant on shearing interaction between fibers, considering the dominant interaction is shearing in a plane problem. Numerical examples show the model’s capacity of reflecting basic failure characteristic in paper. Influences of fiber length and the ratio of fiber strength to bond strength are analyzed in detail.     

Prediction of buckling characteristics of carbon nanotubes

In this paper, to investigate the buckling characteristics of carbon nanotubes, an equivalent beam model is first constructed. The molecular mechanics potentials in a C–C covalent bond are transformed into the form of equivalent strain energy stored in a three dimensional (3D) virtual beam element connecting two carbon atoms. Then, the equivalent stiffness parameters of the beam element can be estimated from the force field constants of the molecular mechanics theory. To evaluate the buckling loads of multi-walled carbon nanotubes, the effects of van-der Waals forces are further modeled using a newly proposed rod element. Then, the buckling characteristics of nanotubes can be easily obtained using a 3D beam and rod model of the traditional finite element method (FEM). The results of this numerical model are in good agreement with some previous results, such as those obtained from molecular dynamics computations. This method, designated as molecular structural mechanics approach, is thus proved to be an efficient means to predict the buckling characteristics of carbon nanotubes. Moreover, in the case of nanotubes with large length/diameter, the validity of Euler’s beam buckling theory and a shell model with the proper material properties defined from the results of present 3D FEM beam model is investigated to reduce the computational cost. The results of these simple theoretical models are found to agree well with the existing experimental results.     

基于弹性力学第一性原理的数据驱动力学建模

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。     

内聚力界面单元与复合材料的界面损伤分析

推导了一种基于内聚力模型无厚的界面单元,用来模拟复合材料纤维与基体之间的界面层．研究了纤维周期分布的复合材料受横向荷载时,在界面不同的强韧性条件下其界面损伤演化的规律和对复合材料整体性质的影响     

Nanoscale finite element models for vibrations of single-walled carbon nanotubes: atomistic versus continuum

By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.