Structural morphology and constitutive behaviour of microheterogeneous materials
Structural morphology and constitutive behaviour of microheterogeneous materials
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DOI：
10.1007/978-3-7091-2662-2_6
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发表时间：
1997-06
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影响因子：
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通讯作者：
A. Zaoui
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文献类型：
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作者：
A. Zaoui
连续介质微观力学的一个主要方面是与这样一个事实有关，即人们通常必须处理不明确的机构：只有部分信息的统计分布的组成相的考虑随机不均匀的材料是available. First章简要报告的主要经典方法，使用这种信息的背景下，线性弹性的界限和估计的推导;然后，将注意力集中在各向同性颗粒复合材料上，特别是Hashin的复合球体组合上。提出了新的估计的整体剪切模量，其中包括Hashin的界限，以及三相模型估计：改进的Hashin-Shtrikman型的界限，从这个分析returtured。第二章提出了证明这种猜测以及推广的方法用于任意的“形态代表模式”，经典的HashinShtrikman变分过程是适应这样的形态分析。在第三章中，我们着重讨论了这种方法的行为方面，特别强调了粘弹性耦合。虽然它是很容易研究的形态特征对线性粘弹性材料的整体行为的影响，这是比较困难的非线性行为：希尔的治疗率独立的经典自洽模型突出和扩展到率相关的行为，但这仍然是一个近似值和新的方法仍有待探索。
One of the main specific aspects of continuum micromechanics is related to the fact that one has generally to deal with ill-defined bodies: only partial information on the statistical distribution of the constituent phases of the considered random inhomogeneous materials is available.The first chapter briefly reports the main classical ways to use such an information in the context of linear elasticity for the derivation of bounds and estimates; attention is then focused on isotropic particulate composites and especially on Hashin’s composite spheres assemblage. New estimates are proposed for the overall shear modulus which include Hashin’s bounds as well as the three-phase model estimate: improved Hashin-Shtrikmantype bounds are conjectured from this analysis.The second chapter presents a proof of this guess as well as a generalization of the method used for arbitrary “morphological representative patterns”; the classical HashinShtrikman variational procedure is adapted to such a morphological analysis. Applications to the derivation of bounds and estimates for the overall elastic moduli are developed both for isotropic and anisotropic distributions of the patterns.In the third chapter, we lay the stress on behavioral aspects of this approach, with special emphasis on the viscoelastic coupling. Whereas it is easy to study the influence of morphological characteristics on the overall behaviour of linearly viscoelastic materials, this is more difficult to do for nonlinear behaviours: Hill’s treatment of the rate-independent classical self-consistent model is highlighted and extended to rate-dependent behaviours but this remains an approximation and new ways have still to be explored.