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纤维排列方式对复合材料总体粘弹性常数的影响   总被引:3,自引:0,他引:3  
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。  相似文献
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许震宇  张若京  何伟 《上海力学》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
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Variational bounds for the effective behavior of nonlinear composites are improved by incorporating more-detailed morphological information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference material with the same microstructure as the nonlinear composite. The geometrical information is contained in the effective properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In this paper, the variational approach is combined with estimates for the effective properties of the reference composite via the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear elastic composite, significantly improving some recent results.  相似文献
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In the present work, we study the overall behavior of a microfractured elastic body within the configurational mechanics framework. Micro and macro scales are considered and scale changes are carried out by asymptotic developments homogenization. The homogenized equations of material momentum and scalar moment of material momentum are obtained. In these equations the microcrack length appears as an internal variable, describing the damage evolution. Both quasistatic and dynamic formulations are presented.  相似文献
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The present paper develops and implements finite element formulation for the asymptotic homogenization theory for periodic composite plate and shell structures, earlier developed in  and , and thus adopts this analytical method for the analysis of periodic inhomogeneous plates and shells with more complicated periodic microstructures. It provides a benchmark test platform for evaluating various methods such as representative volume approaches to calculate effective properties. Furthermore, the new numerical implementation (Cheng et al., 2013) of asymptotic homogenization method of 2D and 3D materials with periodic microstructure is shown to be directly applicable to predict effective properties of periodic plates without any complicated mathematical derivation. The new numerical implementation is based on the rigorous mathematical foundation of the asymptotic homogenization method, and also simplicity similar to the representative volume method. It can be applied easily using commercial software as a black box. Different kinds of elements and modeling techniques available in commercial software can be used to discretize the unit cell. Several numerical examples are given to demonstrate the validity of the proposed methods.  相似文献
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In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.  相似文献
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We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.  相似文献
8.
具有轴向周期微结构的复合梁结构,通常在宏观上简化为一维欧拉-伯努利梁。由于缺乏基于严格数学理论、同时考虑降维及均匀化的等效性能计算方法,已有研究或采用基于平截面假定的弯曲能量近似方法,或采用基于三维周期性介质等效性质的方法。本文首先介绍了基于一维周期性梁的渐近均匀化理论求解新方法,并在此基础上与上述两种方法进行比较。结果表明,基于平截面假定的近似方法忽视了这类梁结构内的三维应力状态,过高地估计了梁的等效性质。  相似文献
9.
Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is devel-oped to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implemen-tation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.  相似文献
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