The effective shear modulus of a random isotropic suspension of monodisperse liquid n -spheres: from the dilute limit to the percolation threshold
The effective shear modulus of a random isotropic suspension of monodisperse liquid n -spheres: from the dilute limit to the percolation threshold
复制标题
单分散液体 n 球的随机各向同性悬浮液的有效剪切模量：从稀释极限到渗滤阈值
DOI：
10.1039/d2sm01219g
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发表时间：
2023
期刊：
影响因子：
3.4
通讯作者：
Lopez-Pamies, Oscar
中科院分区：
文献类型：
--
作者：
Ghosh, Kamalendu;Lefèvre, Victor;Lopez-Pamies, Oscar
本文对弹性体中具有相同初始半径A的随机各向同性液体n球夹杂物（n = 2,3）的宏观或均匀力学响应进行了数值和分析研究。当弹性体是各向同性不可压缩的线弹性固体，构成包裹体的液体是不可压缩的线弹性流体，并且将固体弹性体与液体包裹体分离的界面具有恒定的初始表面张力γ时，注意仅限于基本情况。对于这类悬浮液，最近已经确定其均质力学响应是标准线弹性固体的力学响应，因此，对于这里感兴趣的特定类型的各向同性不可压缩悬浮液，可以仅用弹性体的剪切模量μ的有效剪切模量n，初始弹性毛细管数eCa = γ/2μA，夹杂物的体积分数c来表征。和空间维度n。本文给出了n在大范围的弹性毛细数eCa和包裹体体积分数c上的数值解——通过最近引入的有限元格式生成。与之互补的是，还引入了n的一个公式，该公式与所有数值解在数量上一致，并且与n在包裹体稀体积分数极限和渗透时的渐近结果一致。所提出的公式具有作为迭代均质解的附加理论优点。
A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n-spherical inclusions (n = 2, 3), each having identical initial radius A, in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ. For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ/2μA, the volume fraction c of inclusions, and the space dimension n. This paper presents numerical solutions—generated by means of a recently introduced finite-element scheme—for n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c. Complementary to these, a formula is also introduced for n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution.