On the effective viscoelastic moduli of two–phase media. II. Rigorous bounds on the complex shear modulus in three dimensions
On the effective viscoelastic moduli of two–phase media. II. Rigorous bounds on the complex shear modulus in three dimensions
复制标题
关于两相介质的有效粘弹性模量 II。三维复剪切模量的严格界限。
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
J. Berryman
中科院分区：
文献类型：
--
作者：
G. Milton;J. Berryman
利用Cherkaev-Gibiansky和Hashin-Shtrikman变分原理，以获得两相粘弹性复合材料在三维中的剪切模量的严格界限。最简单的一类边界区域由复平面中的圆组成，该复平面包含与组分的粘弹性模量相关的四个点。通过求所有这些圆的交点，我们得到了复剪切模量的严格界。一个紧凑的算法计算这个区域的交集制定和测试。使用该方法计算的边界集的几个例子。当相位具有相等的和真实的泊松比时，边界集在复剪切模量平面上退化为简单的透镜形区域。两种粘性流体的混合物和粘性流体中固体颗粒的悬浮液为已经计算的边界的另外两个示例提供了物理动机。在所有组分模量都是真实的的重要极限情况下，新的剪切模量界被精确地简化为著名的Hashin-Shtrikman-Walpole界。
Cherkaev–Gibiansky and Hashin–Shtrikman variational principles are utilized in order to obtain rigorous bounds on the shear modulus of two‐phase viscoelastic composites in three dimensions. The simplest class of bounding regions is composed of circles in the complex plane containing four points related to the viscoelastic moduli of the constituents. By taking the intersection of all such circles, we obtain tight bounds on the complex shear modulus. A compact algorithm for computing this region of intersection is formulated and tested. Several examples of bounding sets computed using the method are presented. When the phases have equal and real Poisson's ratio, the bounding set reduces to a simple lens-shaped region in the complex shear modulus plane. A mixture of two viscous fluids and a suspension of solid particles in a viscous fluid provide physical motivations for two other examples of bounds that have been computed. In the important limiting case when all the constituent moduli are real, the new shear modulus bounds are shown to reduce precisely to the well‐known Hashin–Shtrikman–Walpole bounds.