Prediction of the anti-plane moduli of solids consisting of a given distribution of unidirectionally aligned elliptic multi-coated fibers with interfacial damage is the focus of this paper. The fibers and their coating layers may be in the order of nano or micro scales. All the constituent phases of the composite are supposed to be described in terms of couple stress elasticity. Accordingly, the bounds for the overall shear moduli of the aforementioned composites are provided by employing the principles of minimum potential and complementary energies. Certain subtleties associated with the elliptic multi-coated fibers for three cases of pure sliding (completely damaged), imperfect (partially damaged), and perfect (undamaged) interface conditions will be discussed. The inherent anisotropy introduced due to the ellipse geometry of the fibers’ cross-sections is addressed. The effects of the ellipse aspect ratio as well as its size, interfacial damage, and rigidity on the effective anti-plane moduli of such composites will be examined.

本文的重点是预测由单向排列的椭圆多涂层纤维的给定分布组成的，具有界面损伤的固体的反平面模量。纤维及其涂层可以为纳米级或微米级。假定复合材料的所有组成相都是根据偶应力弹性来描述的。因此，通过采用最小电势和互补能量的原理来提供上述复合材料的总剪切模量的界限。对于纯滑动（完全损坏），不完美（部分损坏）和完美（未损坏）界面条件的三种情况，将讨论与椭圆形多涂层纤维相关的某些细微差别。解决了由于纤维横截面的椭圆形几何形状而引起的固有各向异性。将研究椭圆长宽比及其尺寸，界面损伤和刚度对此类复合材料有效反平面模量的影响。