Hashin–Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects
Hashin–Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects
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DOI：
10.1016/j.commatsci.2010.02.027
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发表时间：
2010-05
影响因子：
3.3
通讯作者：
S. Brisard;L. Dormieux;D. Kondo
中科院分区：
文献类型：
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作者：
S. Brisard;L. Dormieux;D. Kondo
纳米复合材料越来越受欢迎，需要力学模型来帮助其设计和优化。这种模型所要解决的关键问题之一是在夹杂物-基体边界处产生的表面应力，由于其高曲率。在本文中，我们表明，与以前所建议的相反，极化技术可以在复合材料的界面效应的背景下。这需要对界面进行特定的数学处理，必须将其视为薄弹性层。然后，我们将建议的一般方法与单分散球形夹杂物的纳米复合材料的具体情况下，体积模量的下限推导。当忽略界面效应时，该界与经典的Hashin-Shtrikman界一致。在界面效应的存在下，我们表明，现有的Mori-Tanaka估计实际上是一个下界的有效体积模量。最后，提出了多分散球形夹杂物纳米复合材料的有效体积模量的下限。虽然这个结果可以被认为是前一个的副产品，但它是新的，没有发表的Mori-Tanaka对应。
Nanocomposites are becoming more and more popular and mechanical models are needed to help with their design and optimization. One of the key issues to be addressed by such models is the surface-stresses arising at the inclusion-matrix boundary, due to its high curvature. In this paper, we show that, contrary to what has previously been suggested, polarization techniques can be employed in the context of composites with interface effects. This requires a specific mathematical treatment of the interface, which must be regarded as a thin elastic layer. We then apply the proposed general methods to the specific case of nanocomposites with monodisperse spherical inclusions, for which a lower bound on the bulk modulus is derived. When interface effects are disregarded, this bound coincides with the classical Hashin–Shtrikman bound. In the presence of interface effects, we show that the existing Mori–Tanaka estimate is in fact a lower bound on the effective bulk modulus. Finally, lower bounds on the effective bulk modulus of nanocomposites with polydisperse spherical inclusions are proposed. Although this result can be considered as a by-product of the previous one, it is new, and has no published Mori–Tanaka counterpart.