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1.
许震宇  张若京  何伟 《力学季刊》2003,24(2):191-197
在某些纤维增强复合材料(FRC)中使用金属或高分子聚合物作为基体材料。在高温等情况下,这类材料具有明显的粘弹性特性。本文采用Riemann—Liouville形式的分数阶导数模型描述基体的粘弹性特性。通过渐近均匀化方法给出了预测FRC整体三维本构关系的解析表达式。给出了应用于基体具有Makris粘弹性关系的具体形式。以圆截面纤维正方形排列的情形为例,给出了等效模量随纤维体积比的变化曲线。结果说明,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。可以看出,在整体的等效模量中包含了局部变形的贡献,局部变形增加了复合材料的耦合刚度。  相似文献   

2.
纤维排列方式对单向纤维加强复合材料弹性常数的影响   总被引:3,自引:0,他引:3  
本文应用GMC方法计算了纤维在规则排列和随机排列时单向纤维加强复合材料的总体弹性系数,结果表明,在一定纤维体积比范围内,虽然纵向弹性模量不受纤维排列方式的影响,但是复合材料的横向弹性模量和横向剪切模量受纤维排列方式的影响较大,所以,在考察复合材料的横向弹性常数时,应该考虑纤维排列方式的影响,在相同纤维比的情况下,正方形排列和正方形对角排列所得的弹性常数是上下界,而六角形排列和随机排列的结果位于以上两者之间,当纤维比较小时(小于20%),纤维的排列方式对各弹性常数均无明显影响,本文的结果在工程应用中有指导意义。  相似文献   

3.
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  相似文献   

4.
罗海安  翟军 《力学学报》1996,28(5):550-557
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  相似文献   

5.
树脂基复合材料粘弹性损伤本构及其实验测定   总被引:2,自引:0,他引:2  
粘弹性是复合材料最重要的力学性能之一。基于Boltsman迭加原理和Schapery非线性粘弹性理论,本文提出了一变量分离式粘弹性本构关系,且由Kachanov“连续性”概念,将损伤变量引入本构关系式中,按不同的加载速度和加载方向对正交玻璃布-环氧材料进行了加、卸载实验研究。根据Lemaitre和Chaboche由宏观弹性常数变化确定损伤量的方法,测得材料的损伤并用一二次函数表示。通过对实验数据的一系列处理方法,确定了材料常数,验证了本文理论的有效性。实验表明,当纤维做为主要承力者时,无粘性产生,材料的损伤和总应变相关而与应变率无关,并得到强度值随应变率增加而升高,极限应变不随应变率变化的结论。  相似文献   

6.
树脂基复合材料板的粘弹性损伤本构关系   总被引:1,自引:0,他引:1  
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  相似文献   

7.
银花  陈宁 《计算力学学报》2012,29(6):966-971
在分析分数阶导数三元件模型理论的基础上,把分数阶导数三元件模型引入有限元模型中,推导出具有分数阶导数三元件本构关系的粘弹性结构动力学有限元格式。同时,应用分数阶导数型粘弹性结构动力学方程的数值算法求解了该有限元格式的数值解。并以二维沥青路面结构为例进行了路面动态粘弹性响应分析。算例分析表明,该方法能够正确有效地进行路面动态粘弹性分析。  相似文献   

8.
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.  相似文献   

9.
李根国  朱正佑 《力学季刊》2001,22(3):346-351
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。  相似文献   

10.
关于复合结构振动分析中粘弹性材料本构方程的形式   总被引:4,自引:1,他引:3  
弹性——粘弹性材料复合结构的振动分析必然要涉及粘弹性材料的本构方程形式。就两种常用的形式:标准形式和分数阶导数形式,本文从粘弹性材料的力学性能曲线拟合和复合结构振动分析两方面比较了这两种本构方程形式的优劣,认为采用标准形式具有更多的优越性。  相似文献   

11.
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.  相似文献   

12.
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.  相似文献   

13.
GENERALSECONDORDERFLUIDFLOWINAPIPEHeGuangyu(何光渝)(DepartmentofPetroleumEngineering,Xi'anPetroleumInstitute,Xi'an710061,P.R.Chi...  相似文献   

14.
This paper presents constitutive models for the anisotropic, finite-deformation viscoelastic behavior of soft fiber-reinforced composites. An essential assumption of the models is that both the fiber reinforcements and matrix can exhibit distinct time-dependent behavior. As such, the constitutive formulation attributes a different viscous stretch measure and free energy density to the matrix and fiber phases. Separate flow rules are specified for the matrix and the individual fiber families. The flow rules for the fiber families then are combined to give an anisotropic flow rule for the fiber phase. This is in contrast to many current inelastic models for soft fiber-reinforced composites which specify evolution equations directly at the composite level. The approach presented here allows key model parameters of the composite to be related to the properties of the matrix and fiber constituents and to the fiber arrangement. An efficient algorithm is developed for the implementation of the constitutive models in a finite-element framework, and examples are presented examining the effects of the viscoelastic behavior of the matrix and fiber phases on the time-dependent response of the composite.  相似文献   

15.
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。  相似文献   

16.
The deformation of a viscoelastic reinforced composite is studied. The composite has an axis of elastic symmetry and consists of transversally isotropic fibers and a viscoelastic matrix, which differ by the volume concentration and mechanical characteristics. The material is modeled by a transversely isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. A plate fabricated from the composite in question is weakened by a through mode I crack and is subjected to constant tensile forces. The viscoelastic properties of the matrix material are described by a convolution operator. The Volterra principle is used to derive expressions for the viscoelastic characteristics and crack opening. The irrational function of the integral operator that describes the crack opening is expanded into an operator continued fraction and is represented as the sum of base operators  相似文献   

17.
A NUMERICAL METHOD FOR FRACTIONAL INTEGRAL WITH APPLICATIONS   总被引:2,自引:0,他引:2  
IntroductionThefractionalcalculushasalonghistoryandthereareamassofworkstodiscussthefractionalderivativesandfractionalintegralswitharbitrary (realorcomplex)order[1- 3 ].Thefractionalcalculushasawideapplicationbackground ,especiallyinthefieldsofchemistry ,electromagnetics,materialscienceandmechanics.Forexample,Gement[4 ]proposedthefractionalderivativeconstitutivemodelsofaviscoelasticmaterialatfirst.Themodelshavereceivedincreasingattention[5 - 7].Onlyafewparametersarecontainedinthemodelsandthemo…  相似文献   

18.
A structural constitutive model that characterizes the active and passive responses of biological tissues with smooth muscle cells (SMCs) is proposed. The model is formulated under the assumption that the contractile units in SMCs and the connected collagen fibers are the active tissue component, while the collagen fibers not connected to the SMCs are the passive tissue component. An evolution law describing the deformation of the active tissue component over time is developed based on the sliding filament theory. In this evolution law the contraction force is the sum of a motor force that initiates contraction, a viscous force that describes the actin–myosin filament sliding, and an elastic force that accounts for the deformation of the cross-bridges. The mechanical response of the collagen fibers is governed by the fiber recruitment process: collagen fibers support load and behave as a linear elastic material only after becoming taut. The proposed structural constitutive model is tested with published active and passive, uniaxial and biaxial experimental data on pig arteries.  相似文献   

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