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1.
戴瑛  嵇醒  Y.-W.  MAI 《力学季刊》2005,26(4):614-617
本文采用交错模型对蒙脱土/尼龙6纳米复合材料的弹性模量进行预测。模型划分为四个区域:以拉伸变形为主的A(蒙脱土片)、B和D区,和同时承受拉伸和剪切两种变形的C区。通过对各区之间合力平衡和变形协调的简单分析,本文得到了封闭形式的蒙脱土/尼龙6纳米复合材料模量预测公式。引用文献[1]中的蒙脱土材料的几何参数和弹性常数,以及纯尼龙6的弹性常数,对纳米复合材料的模量进行预测,预测结果与实验结果基本吻合。有限元法对交错模型的分析证实了理论模型中变形区划分的合理性,同时也发现FEM的预测结果与实验更为接近。  相似文献   

2.
考虑老化的混凝土粘弹性分数导数模型   总被引:11,自引:1,他引:10  
混凝土是一种具有分形结构的材料。采用分数微积分模型来研究具有分形结构材料的老化规律目前尚未见到。本文的目的是采用含分数阶导数的类标准线性体来模拟考虑老化的混凝土的蠕变和松弛规律。给出了分数导数与Abel核之间的关系。讨论了类标准线性体的蠕变柔量和松弛模量及其在考虑老化的混凝土中的应用。与传统的混凝土流变模型相比较表明,类标准线性体可以更好地同时拟合混凝土在不同龄期的蠕变和松弛曲线。而且其形式简单、统一,在计算过程中需要调整的参数很少。可以预见,类标准线性体在混凝土的结构设计和计算中将有着广泛的应用前景。  相似文献   

3.
针对Riemann-Liouville分数阶导数定义的不足之处进行了改进,利用改进过的分数阶导数定义,建立了类Kelvin体粘弹性本构模型,并应用于某固体推进剂上,对本构方程中的三个参数进行了求解,与经典的prony级数模型进行比较,采用分数阶导数的类Kelvin体粘弹性本构模型与实验结果能很好地吻合.  相似文献   

4.
本文研究了放置在黏弹性Pasternak地基上的Timoshenko梁在移动载荷作用下的动力响应行为.首先,引入分数阶导数,将整数阶标准固体黏弹性地基模型推广为分数阶标准固体黏弹性模型.对于Pasternak地基,考虑压缩层是黏弹性的而剪切层仍是弹性的情况,给出了地基反作用力.然后,求解了Timoshenko梁的自由振动解,获得含黏性耗散信息的复固有频率及振型函数.在此基础上用振型叠加法分析了在移动简谐荷载作用下梁的位移响应.在数值算例中,给出了不同分数阶导数、地基黏性系数以及载荷移动速度下梁的动态响应,讨论了黏弹性地基对梁的动态响应的影响规律.  相似文献   

5.
黏弹性材料等效分数阶微观结构标准线性固体模型   总被引:5,自引:3,他引:2  
徐业守  徐赵东  葛腾  徐超 《力学学报》2017,49(5):1059-1069
从黏弹性材料微观链结构出发,以橡胶基黏弹性材料超弹性理论分子网链高斯(Gauss)统计模型和黏滞流动理论为基础,研究黏弹性材料的微观结构、填料等对黏弹性性能的影响.用温频等效原理描述温度对黏弹性材料力学性能的影响,建立了可以有效描述黏弹性材料耗能特性的等效分数阶微观结构标准线性固体模型.采用动态热机械分析仪(DMA)对高聚物黏弹性材料力学性能、耗能能力进行测试.试验表明:在低温区域,储能模量较大,随着温度的升高,储能模量下降显著;能量损耗因子在高温和低温区域数值较小,在玻璃化转变温度附近数值较高.根据测试数据对所提等效分数阶微观结构标准线性固体模型进行验证,该力学模型能够较好地描述黏弹性材料储能模量和能量损耗因子随温度的变化趋势.用9050A和ZN22黏弹性材料对模型的有效性进一步验证,结果表明:9050A和ZN22黏弹性材料具有较好的耗能能力,所提出的等效分数阶微观结构标准线性固体模型能够准确地描述微观结构和填料对黏弹性材料宏观性能的影响,能够准确地描述黏弹性材料在不同温度和频率下的动态力学性能.  相似文献   

6.
衬砌和土体具有黏弹性性质.将土骨架和衬砌结构视为具有分数阶导数本构的黏弹性体,在频率域内研究了深埋圆柱形隧洞衬砌和土体系统的动力特性.基于黏弹性理论,根据界面连续性条件,分别得到了黏弹性土体和衬砌结构的径向位移、应力等的解析表达式.在此基础上,对比分析了经典弹性土和弹性衬砌系统、分数导数黏弹性衬砌和土体系统的动力特性.考察了土体和衬砌的模量比、衬砌厚度、分数导数阶数、材料参数比对系统动力响应的影响.结果表明:经典弹性土和弹性衬砌系统与分数导数黏弹性衬砌和土体系统的动力特性存在较大差异.随着分数导数阶数的增加,衬砌的径向位移和环向应力幅值明显减小;土体的黏性对系统动力特性的影响大于衬砌黏性的影响.  相似文献   

7.
基于非局部理论和分数阶导数理论,研究上覆黏弹性场地土的地震放大效应。利用Eringen非局部理论考虑土体颗粒尺度等非局部效应的影响,通过分数阶黏弹性本构模型刻画场地土的应力应变本构关系,建立基于非局部理论的分数阶黏弹性场地土的振动微分方程;考虑分数阶导数的性质和黏弹性场地土的边界条件,得到了简谐地震波作用下黏弹性场地土的位移和剪切应力的解析解,并在频率域内给出了位移放大系数和应力放大系数的表达式;最后通过数值算例分析了非局部效应、分数阶导数的阶数和土体黏性参数等对黏弹性场地地震放大效应的影响。数值分析结果表明,在低频时位移放大系数和应力放大系数随频率变化曲线存在波动,高频时逐渐趋于稳定;非局部效应对场地土位移放大系数的影响与频率有关,对应力放大系数的影响较大,在研究场地土振动效应时有必要考虑土体非局部效应的影响;分数阶导数的阶数越小,位移放大系数和应力放大系数随频率变化曲线波动越大;场地土的力学性质对场地土的振动效应的影响较大;上覆场地土的黏性对位移放大系数的影响与频率有关,高频时,土体黏性越大,位移放大系数越大;越接近基岩,土体的应力放大系数越大,且土体深度对应力放大系数的影响越大。  相似文献   

8.
采用半解析方法对外部荷载和内部汇项共同作用所诱发的分数阶导数黏弹性饱和土一维固结特性进行了研究。首先,将分数阶微积分理论引入Kelvin-Voigt黏弹性模型以表征饱和黏土的流变性;然后利用Laplace积分变换,解析求解了Laplace变换域内存在外部荷载和内部汇项的分数阶导数Kelvin-Voigt黏弹性饱和土体一维固结微分方程;并采用Crump数值解法实现Laplace数值逆变换,从而得到了物理空间一维固结问题的半解析解。将所得半解析解与经典弹性饱和土体一维固结的解析解及均布荷载(无内部汇项)所诱发的分数阶导数黏弹性饱和土一维固结的解析解进行了对比,验证了本文半解析解的有效性。最后开展了参数研究,讨论了分数阶导数阶次、固结系数和汇项强度对饱和黏土固结行为的影响。结果表明:分数阶导数阶次主要影响固结发展速率,分数阶导数阶次越大,饱和黏土达到固结稳定所需的时间越短;固结系数对存在内部汇项诱发的固结问题的影响与传统由荷载诱发的固结问题的影响不同。固结系数、汇项强度和汇项位置均主要影响饱和黏土的最终沉降量,固结系数越大,最终沉降量越小;汇项强度越大或汇项位置离透水边界越远,固结沉降量越大。且存在汇项后,双面排水条件下的最终沉降量小于单面排水条件下的最终沉降量。  相似文献   

9.
黏弹性准饱和土中球空腔动力特性   总被引:2,自引:0,他引:2  
高华喜  闻敏杰 《力学学报》2012,44(4):753-761
在频率域内研究了内水压力作用下分数导数型黏弹性准饱和土中球空腔的稳态动力响应. 通 过引入与孔隙率有关的应力系数合理地确定了介质和孔隙水共同承担的内水压力值. 将土骨 架和衬砌分别视为具有分数导数本构模型的黏弹性体和多孔柔性材料, 基于Biot两相介质模 型, 通过引入位移势函数解耦得到了内水压力作用下分数导数型黏弹性准饱和土中半封闭球 形空腔的位移、应力和孔隙水压力解析表达式. 考察了物性和几何各参数对球形空腔动力响 应的影响, 结果表明: 分数导数本构模型更合理地描述了土体的动力学行为; 饱和度对应力 和孔隙水压力影响较大, 而对位移影响较小.  相似文献   

10.
在频率域内研究了黏弹性土层中端承桩纵向振动的动力特性.将土骨架视为具有分数阶导数本构关系的黏弹性体,基于黏弹性理论,采用平面应变模型给出了分数阶导数黏弹性土层的动力阻抗.考虑桩纵向振动时的横向惯性效应,将桩等效为Rayleigh-Love杆,得到了桩头动力复刚度和导纳的解析表达式.通过数值计算,分析了不同模型土条件下桩头动刚度因子和阻尼随激励频率的动力响应.同时,研究了Rayleigh-Love和Euler-Bernoulli两种模型桩动力特性的差异.分析了桩-土界面连续性模型和相对滑移模型对黏弹性土层中桩纵向振动的影响.结果表明:1随着阶数和材料参数比的增加,桩头刚度因子和阻尼明显减小;2对于大直径桩,随着外荷载激励频率的增加,桩横向效应对刚度因子和阻尼有显著影响.3连续性模型条件下桩头的刚度因子和阻尼在共振时的振幅小于相对滑移模型条件.  相似文献   

11.
In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter \(\nu > -1\). Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times.  相似文献   

12.
Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melts, using a fractional model. In this paper the authors propose an advanced model for capturing the non-linear trend of the shear viscosity of polymer melts as function of the shear rate. Results obtained with the fractional model are compared with those obtained using a classical model which involves classical Maxwell elements. The comparison between experimental data and the theoretical model shows a good agreement, emphasizing that fractional model is proper for studying viscoelasticity, even if the material exhibits a non-linear behavior.  相似文献   

13.
刘五祥  张胡靓  吴玥 《力学季刊》2022,43(2):416-422
本文研究了基于时序参数法的玄武岩纤维增强复合材料(BFRP)板弯曲蠕变行为.为了提高模型理论预测的精度,文中将整个实验时长的数据进行了合理的细化分组,且每组时长尽可能相同,然后对细化分组的数据组分别进行直接外推法拟合,得到各数据组对应的拟合方程参数,最后获得了BFRP板弯曲蠕变行为的理论预测模型.对比模型预测值和实验值可以发现:模型预测值随着时间的增长,越来越接近于实验值,最后二者的相对误差几乎为零.该结果表明:文中建立的蠕变预测模型具有足够高的精度,可以应用于BFRP的蠕变行为的预测.  相似文献   

14.
In this paper, we make the first attempt to apply the fractal derivative to modeling viscoelastic behavior. The methodology of scaling transformation is utilized to obtain the creep modulus and relaxation compliance for the proposed fractal Maxwell and Kelvin models. Comparing with the fractional derivatives reported in the literature, the fractal derivative as a local operator has lower calculation costs and memory storage requirements. Moreover, numerical results show that the proposed fractal models require fewer parameters, have simpler mathematical expression and result in higher accuracy than the classical integer-order derivative models. Results further confirm that the proposed fractal models can characterize the creep behavior of viscoelastic materials.  相似文献   

15.
Generally, the complex behaviour of the disc of the temporomandibular joint (TMJ) cannot be adequately represented using linear elastic or linear viscoelastic models. Since the disc is regularly subjected to large strain and stress levels, the study of its non-linear response under compression is of practical interest, especially for analysis of medical dysfunctions. With this aim, relaxation and creep tests were carried out using round specimens of diameters ranging between 4 and 6 mm cut off from the central, anterior, posterior, lateral and medial zones of porcine discs to investigate the regional mechanical properties differences. The experimental data results are fitted using Prony series, based on generalized Maxwell and Kelvin models, allowing the relaxation and creep moduli to be represented, respectively, as a function of the strain and stress. The results show that the non-linear material behaviour of this biological tissue is properly described by the proposed models, to be considered subsequently in numerical calculations.  相似文献   

16.
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   

17.
In order to predict the mechanical performance of the polyvinyl chloride(PVC) at a high operating temperature,a series of short-term tensile creep tests(onetenth of the physical aging time) of the PVC are carried out at 63 C with a small constant stress by a dynamic mechanical analyzer(DMA).The Struik-Kohlrausch(SK) formula and Struik shifting methods are used to describe these creep data for various physical aging time.A new phenomenological model based on the multiple relaxation mechanisms of an amorphous polymer is developed to quantitatively characterize the SK parameters(the initial creep compliance,the characteristic retardation time,and the shape factor) determined by the aging time.It is shown that the momentary creep compliance curve of the PVC at 63 C can be very well fitted by the SK formula for each aging time.However,the SK parameters for the creep curves are not constant during the aging process at the elevated temperatures,and the evolution of these parameters and the creep rate versus aging time curves at the double logarithmic coordinates have shown a nonlinear phenomenon.Moreover,the creep master curves obtained by the superposition with the Struik shifting methods are unsatisfactory in such a case.Finally,the predicted results calculated from the present model incorporating with the SK formula are in excellent agreement with the creep experimental data for the PVC isothermally aged at the temperature relatively close to the glass transition temperature.  相似文献   

18.
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   

19.
Fading memory is a distinguishing characteristic of viscoelastic solids. Its assessment is often achieved by measuring the stress due to harmonic strain histories at different frequencies: from the experimental point of view, the storage and loss moduli are, hence, introduced. On the other side, the mathematical modeling of viscoelastic materials is usually based on the consideration of a kernel function whose decay rate is sufficiently fast. For several different solid materials, we have collated experimental evidence showing an high sensitivity to frequency variations of both the storage and loss moduli. By contrast, we prove that the commonly employed viscoelastic kernels (Prony series, continuous kernel, etc.) cannot reproduce this experimental behavior, as the resulting frequency sensitivity of the storage modulus is always zero when assessed at low frequency. This leads to identification problems of the material parameters which are strongly ill conditioned. However, we identify the specific kernel property which is responsible for this misbehavior: the long-term material memory must not decrease too fast. Some viscoelastic kernels, showing the correct memory??s rate of decay, are introduced and their improved ability to match the experimental data analyzed.  相似文献   

20.
According to the elastic-viscoelastic correspondence principle, an elastic microme- chanical framework taking the inclusion-matrix interface effect into account is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded in a viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different temperature and stress conditions in order to determine the matrix constitutive parameters, the framework presented is validated by comparison with the experiment, and then some predictions of uniaxial compression creep behavior of asphalt mixture in different temperature and stress conditions are given.  相似文献   

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