An active composite material is assumed to be composed of a passive isotropic elastic matrix with spherical voids containing active rod-like elements, each of which being in diametrical contact with the void’s surface. A ball-bearing fixation between the rod and the contact pads is assumed, and thereby the normal contact becomes a primary mode through which the rod-like elements transfer active loading to the surrounding elastic matrix. Under the assumption that the radius of contact pads is small compared to the void radius, an asymptotic solution to the corresponding elasticity polarization matrix has been derived by the method of matched asymptotic expansions. The obtained explicit analytical results for the matrix/inclusion contact problem and a non-interaction approximation scheme are utilized for constructing an asymptotic model of the dilute elastic active microstructure.

中文翻译：

---

弹性活性物质 — 一种基于非相互作用近似的复合力学方法


假设有源复合材料由无源各向同性弹性基体组成，球形空隙包含有源棒状元件，每个元件都与空隙表面截然接触。假设杆和接触垫之间的滚珠轴承固定，因此法向接触成为杆状元件将主动载荷传递到周围弹性基体的主要模式。假设接触垫的半径与空隙半径相比较小，通过匹配渐近展开的方法推导出了相应弹性极化矩阵的渐近解。所获得的基体/夹杂物接触问题的显式解析结果和非相互作用近似方案用于构建稀弹性活性微观结构的渐近模型。