Radially transverse isotropic inclusions in homogeneous isotropic elastic host media are considered. Mellin transform method is used for solution of the volume integral equation of the problem for an isolated inclusion subjected to a constant external stress (strain) field. The tensor structure of the solution is revealed with precision to three scalar functions of the radial coordinate, and the system of ordinary differential equations for these functions is derived. For multilayered radially transverse isotropic inclusions with constant elastic coefficients inside layers, explicit solution of these equations is obtained. An efficient numerical algorithm of solution for inclusions with an arbitrary number of the layers is proposed. Neutral inclusions that do not disturb homogeneous external fields applied to the medium are considered. It is shown that an inclusion with an isotropic core and radially transverse isotropic external layer can be weak neutral by appropriate choice of the layer elastic constants. The effective field method is used for determination of the effective elastic stiffness tensor of a homogeneous isotropic medium containing a random set of radially transverse isotropic inclusions.

中文翻译：

---

各向同性弹性介质中的径向横向各向同性夹杂物：局部场、中性夹杂物、有效弹性特性


考虑均匀各向同性弹性主体介质中的径向横向各向同性夹杂物。梅林变换方法用于求解恒定外应力（应变）场作用下的孤立夹杂物问题的体积积分方程。精确地揭示了径向坐标的三个标量函数解的张量结构，并推导了这些函数的常微分方程组。对于层内弹性系数恒定的多层径向横向各向同性夹杂物，得到了这些方程的显式解。提出了一种求解任意层数夹杂物的高效数值算法。考虑不干扰施加到介质的均匀外部场的中性夹杂物。结果表明，通过适当选择层弹性常数，具有各向同性核心和径向横向各向同性外层的夹杂物可以是弱中性的。有效场方法用于确定包含一组随机的径向横向各向同性夹杂物的均匀各向同性介质的有效弹性刚度张量。