纤维排列方式对复合材料总体粘弹性常数的影响

对于金属基或高分子聚合物基复合材料，在特定情况下会表现出明显的粘弹性特性。本文采用Riemann—Liouville形式的分数阶导数模型描述基体的粘性特性，通过渐进均匀化方法给出了预测纤维加强复合材料整体本构关系的解析表达式，给出应用于基体具有Makris粘弹性关系的具体形式。最后，考察了圆截面纤维正方形排列和对角排列时的总体粘弹性弹性常数随纤维比的变化曲线。结果表明，这类复合材料仍具有粘弹性特性，其整体粘弹性本构关系的弹性部分综合了纤维弹性和基体弹性的贡献，粘性部分来自基体粘性的贡献，复合材料具有和基体相同的粘性系数和分数阶。为分析微结构特征对整体特性的贡献，须求解两类局部问题。在相同纤维体积比情况下，正方形排列的总体弹性系数大于正方形对角排列，而粘性常数相反。     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

分数阶粘弹性地基上薄板波动和振动特性分析

本文研究了粘弹性地基上薄板的波动和振动问题．主要讨论了基于分数导数理论的粘弹性地基模型上 薄板弯曲波的传播特性以及固有频率对地基的依赖特性．推导了三种经典粘弹性地基模型的复模量．并利用分 数导数的性质得到分数阶粘弹性地基上 Kirchhoff板中弯曲波的传播速度、衰减系数以及自由振动的复固有频 率．数值算例表明粘弹性地基对弯曲波传播特性存在显著影响,不同粘弹性模型所对应的色散和衰减特性也存 在较大差别．分数阶导数可以实现相邻整数阶导数之间的光滑过渡．利用分数导数的本构关系可以更加真实地 描述粘弹性地基的历史依赖行为,更准确地表现出粘弹性地基板中弯曲波的色散和衰减特性．     

基于等效特征应变原理的复合材料有效模量细观力学分析

基于等效特征应变原理,提出了一种新的复合材料有效模量细观力学分析方法。首先,在等效特征应变原理基础上提出平均等效特征应变原理,它可用于解决有限体下任意形状(无论是凸或凹形)的单个夹杂或多个夹杂的弹性变形问题。其次,将平均等效特征应变原理与细观力学直接均匀法相结合,来分析确定复合材料的有效模量。最后利用复合材料纤维与基体的力学性能参数及纤维的体分比,借助MATLAB编程方法,预测其有效模量。通过将理论预测值与已有的的试验值、其它理论预测值进行对比,验证了新分析方法的合理性和分析精度。     

舰用轻型复合装甲结构及其抗弹实验研究

采用纤维增强复合材料(简称FRC)板前置船体结构钢(简称C型钢)板模拟舰用轻型复合装甲结构,对有间隙和无间隙复合装甲结构以及不同纤维增强复合材料防弹板进行了打靶实验研究,实验测试了不同纤维增强复合材料防弹板以及有间隙和无间隙复合装甲结构抗弹丸穿甲的吸能量。结果表明:FRC板较C型钢板有明显的抗弹优势;弹丸速度和形状对FRC板的抗弹性能有较大影响;基体种类和基体含量对FRC板的抗弹性能有一定影响;FRC板与C型钢板之间间距的增大将有利于组合靶板综合抗弹能力的提高。     

树脂基复合材料板的粘弹性损伤本构关系

1 引言一般树脂基复合材料板具有相当强烈的各向异性和非均匀性,受载后很容易发生基体裂纹群等损伤.同时,即使在常温下,这类材料也显示粘弹性.而且,损伤与粘弹性都是各向异性的.因此,复合材料力学响应的分析比均匀无损的粘弹性材料要复杂得多,困难得多.实际上,在复合材料的结构强度和尺寸稳定性设计中,它的时间相关性和存在损伤是两个不能回避的重要问题.为此,特别需要复合材料粘弹性损伤本构关系的知识.最近一个时期,复合材料的粘弹性本构关系已得到一定的研究.作者曾提出适用于复合材料分析的弹脆性损伤模型以及考虑损伤的粘弹性本构关系.在此基础     

均匀化方法在粘弹性多层复合材料中的应用

主要研究了由各向同性线弹性加强体和各向同性线粘弹性基体组成的多层复合材料的问题,在已有的线弹性多层材料的均匀化方法的基础上,应用弹性一粘弹性对应原理,在Carson域中求解粘弹性多层材料的问题。通过Burgers模型表示线粘弹性基体材料,反演得到了多层材料的有效松弛模量和有效泊松比在时间域中的表达式,并且与实验结果和其他结果进行了比较。     

基于Riesz势空间分数阶算子的非局部粘弹性力学元件

将幂函数引入Eringen非局部线粘弹性本构,导出Riesz势形式的应力-应变关系。利用该关系,构造非局部弹簧和非局部阻尼器两类元件;利用元件的串联和并联,建立非局部Kelvin和非局部Maxwell粘弹性模型,推导模型的松弛模量和蠕变柔量。进一步,给出非局部粘弹性模型在生物组织超声波耗散建模中的应用。     

基于复数神经网络的粘弹性材料动态模量拟合方法

固体火箭发动机药柱粘弹性材料除具有弹塑性特性,还具有粘滞性,这一特性使得材料变形具有明显的时间效应,本构关系复杂,进行动态力学分析时,动态模量难以有效拟合．本文提出了一种基于(Levenberg-Marquardt, L-M)算法的复数神经网络拟合粘弹性材料动态模量的方法．通过广义Maxwell模型推导得到材料的动态模量表达式,以此构造未定网络参数为复数的神经网络,从而提供了一种输入、输出样本均为复数的神经网络解决方法．将实数L-M训练算法进行改进,衍生到复数领域,提出复数L-M训练算法．通过粘弹性材料实验,将实验数据时温等效转换,获得复数神经网络的训练及测试样本．通过对神经网络进行训练,实现粘弹性材料动态模量的高精度拟合．数值算例表明,与传统神经网络拟合方法相比,所提方法在训练速度和泛化能力方面都有其优越性．     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.     

VISCOELASTIC CONSTITUTIVE MODEL RELATED TO DEFORMATION OF INSECT WING UNDER LOADING IN FLAPPING MOTION

Flexible insect wings deform passively under the periodic loading during napping flight. The wing flexibility is considered as one of the specific mechanisms on improving insect flight performance. The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet. A viscoelastic constitutive relation model was established based on the stress relaxation experiment of a dragonfly wing (in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping. It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one. The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.     

A numerical method for fractional integral with applications

IntroductionThefractionalcalculushasalonghistoryandthereareamassofworkstodiscussthefractionalderivativesandfractionalintegralswitharbitrary (realorcomplex)order[1- 3 ].Thefractionalcalculushasawideapplicationbackground ,especiallyinthefieldsofchemistry ,electromagnetics,materialscienceandmechanics.Forexample,Gement[4 ]proposedthefractionalderivativeconstitutivemodelsofaviscoelasticmaterialatfirst.Themodelshavereceivedincreasingattention[5 - 7].Onlyafewparametersarecontainedinthemodelsandthemo…     

GENERAL SECOND ORDER FLUID FLOW IN A PIPE

ＧＥＮＥＲＡＬＳＥＣＯＮＤＯＲＤＥＲＦＬＵＩＤＦＬＯＷＩＮＡＰＩＰＥＨｅＧｕａｎｇｙｕ（何光渝）（ＤｅｐａｒｔｍｅｎｔｏｆＰｅｔｒｏｌｅｕｍＥｎｇｉｎｅｅｒｉｎｇ，Ｘｉ＇ａｎＰｅｔｒｏｌｅｕｍＩｎｓｔｉｔｕｔｅ，Ｘｉ＇ａｎ７１００６１，Ｐ．Ｒ．Ｃｈｉ...     

Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives

Fractional time derivatives are used to deduce a generalization ofviscoelastic constitutive equations of differential operator type. Theseso-called fractional constitutive equations result in improvedcurve-fitting properties, especially when experimental data from longtime intervals or spanning several frequency decades need to be fitted.Compared to integer-order time derivative concepts less parameters arerequired. In addition, fractional constitutive equations lead to causalbehavior and the concept of fractional derivatives can be physicallyjustified providing a foundation of fractional constitutive equations.First, three-dimensional fractional constitutive equations based onthe Grünwaldian formulation are derived and their implementationinto an elastic FE code is demonstrated. Then, parameter identificationsfor the fractional 3-parameter model in the time domain as well as inthe frequency domain are carried out and compared to integer-orderderivative constitutive equations. As a result the improved performanceof fractional constitutive equations becomes obvious. Finally, theidentified material model is used to perform an FE time steppinganalysis of a viscoelastic structure.     

非线性粘弹性Timoshenko梁动力学行为的分布

本文讨论了有限变形粘弹性Timoshenko梁的动力学行为。首先由Timoshenko梁的理论和分数导数型本构关系给出了梁的控制方程。其次为了便于求解,采用Galerkin方法对系统进行了简化,并比较了1阶和2阶截断系统的动力学性质,它们具有相同的定性性质,说明Galerkin方法的合理性。给出了求解包含分数积分的积分－微分方程的一种新方法,以便求解系统的长时间的解。综合利用非线性动力系统中的经典方法,揭示了梁在有限变形情况下丰富的动力学行为,并分别考察了载荷参数的材料参数对结构的动力学行为的影响。     

半封闭分数导数粘弹性衬砌隧道的频域响应

混凝土衬砌具有粘弹性性质,以往的经典Kelvin模型、弹性理论和壳体理论都不能刻画其蠕变的全过程。本文基于饱和多孔介质理论,在频率域研究了轴对称荷载和流体压力作用下饱和粘弹性土中半封闭分数导数型衬砌隧洞的稳态动力响应。在引入隧洞部分透水边界条件的基础上,通过分数阶导数粘弹性模型描述衬砌的应力—位移本构关系,并利用衬砌内边界以及接触面的连续性条件,得到了饱和土和衬砌的应力、位移和孔压解答。考察了分数导数阶数、材料参数以及衬砌和土体相对渗透系数的影响。研究表明：分数导数阶数对系统响应影响较大,且依赖于衬砌的材料参数。另外,相对渗透系数对系统响应的影响很大。