A technique for determination of viscoelastic characteristics of transversal-isotropic fiber composite with isotropic components – viscoelastic matrix and elastic fiber – is proposed. The compositeunity cell consisting of two infinite coaxial cylinders is investigated by the representative element method. The solid and hollow cylinders are used to simulate the fiber and matrix, respectively. Characteristics of isotropic components of the composite are expressed through the bulk and shear moduli. The viscoelastic properties of the matrix and the homogenized composite are modeled by integral ratios of the hereditary Volterra theory. The Laplace transform is used to find the components of the axisymmetric stress-strain state of the cell and its components under uniform longitudinal tension. This make it possible to replace integral operators by algebraic functions. The effective rheological characteristics of a transversal-isotropic viscoelastic composite are determined by fitting displacements of a representative element of the viscoelastic composite and its components.

提出了一种确定具有各向同性成分（粘弹性基体和弹性纤维）的横向各向同性纤维复合材料的粘弹性特性的技术。通过代表元方法研究了由两个无限同轴圆柱体组成的复合单元。实心和空心圆柱体分别用于模拟纤维和基质。复合材料的各向同性组分的特性通过体积模量和剪切模量表示。基体和均质复合材料的粘弹性是通过遗传沃尔泰拉理论的积分比来建模的。拉普拉斯变换用于在均匀的纵向张力下找到单元的轴对称应力-应变状态的分量及其分量。这使得可以用代数函数代替积分算子。横观各向同性粘弹性复合材料的有效流变特性由粘弹性复合材料及其成分的代表元素的位移确定。