Analysis of bending and buckling of pre-twisted beams: A bioinspired study

Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elas- tic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self- weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.     

Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices

In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However, when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in the 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation, which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is applied for the homogenization of a triangular chiral lattice, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are verified by the exact solution of the discrete model.     

Handedness-dependent hyperelasticity of biological soft fibers with multilayered helical structures

Collagen fibrils with multilayered helical structures widely exist in biological soft tissues, e.g., blood vessels, tendons, and ligaments. Understanding the mechanical properties of this kind of chiral materials is not only essential for evaluating the mechanical behaviors of the host tissues but also of significance for medical engineering, clinical diagnosis, and surgical operation. In this paper, a theoretical model is presented to investigate the hyperelasticity of biological soft fibers with multilayered helical structures. The effects of the initial helical angle, number and handedness of the fibers in each ply on the mechanical response of the material are examined. Our analysis reveals a switch of contact modes between two neighboring layers, which may greatly alter the overall non-linear response of the material. The Poisson׳s ratio of such a multilayered string can be greater than 0.5. The obtained results agree with relevant experiments of soft tissues. This work sheds light on the non-linear mechanics of chiral materials and may also guide the design of biomimetic materials.     

The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes

The effects of chirality and boundary conditions on the elastic properties and buckling behavior of single-walled carbon nanotubes are investigated using atomistic simulations. The influences of the tube length and diameter are also included. It is found that the elastic properties of carbon nanotubes at small deformations are insensitive to the tube chirality and boundary conditions during compression. However, for large deformations occurred upon both compression and bending, the tube buckling behavior is shown to be very sensitive to both tube chirality and boundary conditions. Therefore, while the popular continuum thin shell model can be successfully applied to describe nanotube elastic properties at small deformation such as the Young’s modulus, it cannot correctly account for the buckling behavior. These results may allow better evaluation of nanotube mechanical properties via appropriate atomistic simulations.     

基因芯片纳米力学行为的能量模型

本文利用能量法研究了无标记生物检测中基因芯片的纳米力学行为.首先,在考虑微悬臂梁机械能和基因层静电能、构型熵、渗透能的情况下,借助Strey通过实验得到的双链DNA(dsDNA)自由能的经验势,建立了DNA纳观几何、物理、化学特征以及芯片几何尺寸、宏观力学性能等因素与基因芯片总能量之间的关系.其次,利用能量最小原理预测了Wu实验中基因芯片的纳米挠度响应.数值计算结果与Wu的实验数据比较表明,芯片的弯曲挠度随着DNA链长的增长而增加,且数值结果与实验数据吻合良好;同时四层梁模型和两层梁模型的比较表明,金层和铬层对芯片纳米挠度的影响不可忽略.     

Analytical solutions for elastic binary nanotubes of arbitrary chirality

Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional outof-plane inversion term into the so-called stick-spiral model,which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of Ⅲ–Ⅴ and Ⅱ–Ⅵ group elements.     

单壁碳纳米管屈曲的原子/连续介质混合模型

用数学和力学研究所，上海 200072)//力学学报.--2004,36(6).--744～748 提供了一种运用原子/连续介质混合(hybrid atomic/continuum,HAC)方法解决纳米力学问题的思路. 通过在连续介质力学模型中引入利用分子力学方法获得物性参数，建立了预测单壁碳纳米管临界屈曲参数的HAC模型. 结果表明, HAC模型具有与连续介质力学模型可比拟的简洁性, 同时可表征纳米管微观结构特征对屈曲参数的影响. 计算结果表明，Zigzag纳米管的抗屈曲性能优于Armchair纳米管. 基于Tersoff-Brenner作用势的分子动力学结果证实了这一结论.     

MECHANICAL BEHAVIOUR OF NATURAL COW LEATHER IN TENSION

We study experimentally the microstructure and mechanical behavior of natural cow leather. Tensile tests are performed using leather strips to observe their deformation, creep and failure. It is found that the microstructure of cow leather is a layered, complicated network of fibers of different sizes from a few to a few hundreds of nanometers in diameter. They show nonlinear stress-strain relations and viscoelastic behavior. The effect of humidity is also examined. A simple theoretical model of a multilayered beam is proposed to describe the most basic behavior in tension.     

Micropolar modeling of planar orthotropic rectangular chiral lattices

Rectangular chiral lattices possess a two-fold symmetry; in order to characterize the overall behavior of such lattices, a two-dimensional orthotropic chiral micropolar theory is proposed. Eight additional material constants are necessary to represent the anisotropy in comparison with triangular ones, four of which are devoted to chirality. Homogenization procedures are also developed for the chiral lattice with rigid or deformable circles, all material constants in the developed micropolar theory are derived analytically for the case of the rigid circles and numerically for the case of the deformable circles. The dependences of these material constants and of wave propagation on the microstructural parameters are also examined.     

A DAMAGE MECHANICS MODEL FOR TWISTED CARBON NANOTUBE FIBERS

Carbon nanotube fibers can be fabricated by the chemical vapor deposition spinning process. They are promising for a wide range of applications such as the building blocks of high-performance composite materials and micro-electrochemical sensors. Mechanical twisting is an effective means of enhancing the mechanical properties of carbon nanotube fibers during fabrication or by post processing. However, the effects of twisting on the mechanical properties remain an unsolved issue. In this paper, we present a two-scale damage mechanics model to quantitatively investigate the effects of twisting on the mechanical properties of carbon nanotube fibers. The numerical results demonstrate that the developed damage mechanics model can effectively describe the elastic and the plastic-like behaviors of carbon nanotube fibers during the tension process. A definite range of twisting which can effectively enhance the mechanical properties of carbon nanotube fiber is given. The results can be used to guide the mechanical twisting of carbon nanotube fibers to improve their properties and help optimize the mechanical performance of carbon nanotube-based materials.     

BUCKING AND FREE VIBRATION OF PIEZOELECTRIC/PIEZOMAGNETIC LAMINATED NANO-BEAM 1)

针对压电/压磁层合纳米梁屈曲、自由振动问题,基于非局部理论与正弦剪切型变形梁理论,建立了力学模型;利用哈密顿原理推导出层合梁运动方程与边界条件;通过数值解法求得层合梁临界屈曲载荷与自由振动频率。对数值结果分析可知：磁电弹夹层对压电/压磁层合纳米梁屈曲和自由振动的影响不能忽略;磁电弹夹层中压电或压磁材料的体积分数和夹层厚度为主要影响因素;分析得到的影响规律可为此类材料在工程中的应用提供理论参考。     

热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论,引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性,研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的,利用能量法推导了矩形截面梁的控制微分方程和边界条件,并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明,对称材料模型下,固支梁与简支梁均显示出了典型的分支屈曲行为特征,而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下,固支梁仍显示出分支屈曲行为特征,但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化;而对于两端简支梁,发生了弯曲变形,弯曲挠度随载荷的增大而增大．     

双周期圆截面纤维复合材料平面问题的解析法

结合双准周期Riemann边值问题理论与Eshelby等效夹杂原理，为双周期圆截面纤维复合材 料平面问题发展了一个实用有效的解析方法，获得了问题的全场级数解并与有限元结果进行 了比较. 该方法为非均匀材料的力学性质分析和复合材料等新材料的微结构设计提供了 一个有效的计算工具，也可用来评估有限元等数值与近似方法的精度.     

Analytical investigation of nonlinear interlaminar fracture in trilayered polymer composite beam under mode II crack loading conditions using the J -integral approach

The present study is concerned with a nonlinear fracture analysis of trilayered beam built up by two unidirectional fiber-reinforced polymer composites. It is assumed that two interlaminar cracks exist between the layers. A tensile force applied to the middle layer generates pure mode II crack loading conditions. The J -integral approach is used to investigate the nonlinear fracture behavior of the beam. The elastic-linearly hardening model is applied to describe the mechanical behavior of the two composites. Sixth expressions for J -integral are derived using a beam theory model. These expressions correspond to the characteristic magnitudes of the external force. The validity of the formulae obtained is proved by comparison with the J -integral solution in the case of linear-elastic behavior of the composite materials. A numerical example is presented in order to demonstrate the ability of the expressions obtained for the analysis of nonlinear fracture in polymer composites.     

The coupled thermomechanical behavior of a three-layer viscoplastic beam under harmonic loading

The coupled thermomechanical behavior of structurally inhomogeneous viscoplastic bodies under cyclic loading is investigated by an example of the problem on harmonic bending and dissipative heat-up of a three-layer beam. Both the generalized thermomechanically consistent flow theory (an exact formulation) and the scleronomic model (an approximated formulation) are used to solve the problem. Aluminum alloy AMg-6 and steel 12KhN3A are chosen as the materials of the layers. The following two configurations of the beam are considered: (i) the outer layers are aluminum and the inner layer is steel, and (ii) the outer layers are steel and the inner layer is aluminum. The results obtained in solving the problem in the exact and approximate formulations are compared for the amplitudes of the mechanical field characteristics, dissipated and accumulated energies, and the temperature of dissipative heat-up. A good agreement between the results is pointed out. A comparative estimation of the absorption factor of the beam for different arrangement of the layers is performed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraines, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 135–143, February, 2000.     

基于离散元的杆件断裂全过程数值模拟

杆件的断裂会涉及到大变形、非线性以及不连续等问题,通常的数值计算方法模拟这种复杂力学行为具有局限性。本文基于颗粒离散元法DEM,将接触粘结处的分布式弹簧用梁纤维进行等效,提出了一种适于结构弹塑性分析的DEM纤维梁模型,然后在此基础上构建了构件断裂模拟算法以及纤维破环准则。将该模型应用于悬臂梁结构,模拟了悬臂梁从弹性到弹塑性阶段,再到断裂破坏的全过程,数值模拟得到的结构响应和截面开裂破坏形态均较合理。最后将该方法应用于单层网壳倒塌破坏模拟,并与网壳振动台倒塌试验进行对比,结果表明,数值模拟得到的杆件断裂过程及结构倒塌模式与试验现象一致,验证了该模型的正确性和适用性。     

火灾下混凝土结构破坏模拟的纤维梁单元模型

为分析和模拟结构构件在火灾下的失效破坏过程,本文基于建筑结构分析中常用的纤维梁单元模型,建立了钢筋混凝土梁、柱构件的火灾破坏数值模型.此模型将构件截面划分成多个纤维,从而可以模拟构件截面的不均匀温度场分布以及高温下混凝土材料的开裂、压碎和钢筋屈服等行为.并根据全拉格朗日描述方法,推导了纤维梁单元的切线刚度矩阵,建立了纤维梁单元的增量求解方程.最后,将本文模型的模拟结果和多个具体试验结果进行了分析比较,进一步验证了模型的可靠性.     

应变梯度Mindlin板边值问题的讨论

实验和分子动力学计算结果表明,当材料/结构的特征尺寸降为微纳米量级时,他们将表现出明显的尺度效应,因此能否建立精确表征其力学行为的连续介质力学模型具有重要的理论和现实意义.尽管现有文献对非经典Mindlin板的力学行为进行了大量研究,但该模型的变分自洽的边值问题是近年来未攻克的科学问题之一.基于简化的应变梯度理论给出了各向同性Mindlin板应变能的表达式,通过变分原理和张量分析,得到了Mindlin板变分自洽的边值问题及其对应角点条件的位移微分表达式.本文Mindlin板模型的边值问题可退化为相应的Timoshenko梁和Kirchhoff板模型的边值问题,验证了本文结果的有效性.研究结果发现,该Mindlin板模型的控制方程是一个解耦后横向振动具有12阶的偏微分方程,因此需要每个板边提供6个边界条件.角点条件由双应力(double stress)产生,并与经典的剪力、弯矩和扭矩沿截面的法向梯度有关.本文首次澄清了应变梯度Mindlin板存在角点条件这一事实,所得的变分结果有望为其有限元法和伽辽金法等数值方法提供理论依据.     

An improved dynamic model for a silicone material beam with large deformation

Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation (ANCF) beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore, dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results, while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam.     

利用结构基因法研究非线性周期性板结构的等效力学性能

非线性周期性板结构是一类在智能复合材料领域具有巨大应用潜力的结构,因其构成材料的非线性特性,以及结构中经常包含增强纤维、肋板和空洞等复杂微结构导致的材料几何非线性,利用常规的有限元方法进行建模和分析较为困难.本文提出了一种结构基因法,通过提取非线性周期性板结构的最小模型单元作为其结构基因,将异质周期性板结构等效为均质板结构,便捷地求解了非线性周期性板结构的微观力学性能和整体等效力学性能.算例表明,结构基因方法可用来分析复杂非线性复合材料结构问题,计算结果精度足够,为复合材料微观力学研究提供了有价值的参考.