Homogenization of A Unidirectional Composite Reinforced with Two Types of Transtropic Hollow Fibers

A method for determining effective elastic constants of a composite unidirectionally reinforced with two types of transtropic hollow fibers is developed. Determining these characteristics is an integral step in the design of composite structures. The approach is based on analytical formulas for determining the elastic characteristics of a two-component composite with a transtropic matrix and hollow fiber. Hexagonal fiber lay-up with periodic reinforcement structure is considered. Double homogenization is used. The composite is conventionally divided into hexagonal regions of two types. The first is a hollow fiber of one material and the surrounding matrix. Similarly, the second one – with a hollow fiber of another material. In the first homogenization, elastic constants of the transtropic material of each of the two regions are determined. In the repeated homogenization, the region of the first type is taken as a “conditional” fiber, the region of the second type is taken as a “conditional” matrix. Effective elastic constants for a composite reinforced with two types of isotropic hollow fibers are calculated. The proposed method gives a good convergence of the results with calculations by known formulas. The maximum relative calculation error for the longitudinal elastic characteristics compared to known formulas does not exceed 0.05 %. The dependences of some effective elastic constants on the volume content of hollow fibers of various types are constructed. Using this approach, three-component composites can be modeled varying the materials of the matrix, hollow fibers and their volume content. This allows predicting the strength of such composites under certain deformations at the design stag