Unit Cell Models of Viscoelastic Fibrous Composites for Numerical Computation of Effective Properties

The paper presents an extension to viscoelastic composites of a former developed numerical homogenization procedure which was used for elastic and piezoelectric material systems. It is based on an unit cell model using the finite element method. In the paper a brief description of the basic equations and the homogenization algorithm with specific attention to the numerical model is given. The investigated composites consist of a viscoelastic matrix with unidirectional embedded cylindrical elastic fibers. Hence the homogenized behavior of the composite is also viscoelastic. Consequently the effective coefficients are time-dependent. The geometrical shape of the unit cell is rhombic which allows to analyze a wide range of nonstandard unidirectional fiber distributions. Otherwise it includes the special cases for square and hexagonal fiber arrangements which can be used for comparisons with other solutions. Here results are compared with an analytical homogenization method. Furthermore the influences of rhombic angle and fiber volume fraction on effective coefficients are investigated. In addition two limit cases are considered. One is with air as inclusions which is equivalent to a porous media and the other is the pure matrix without fibers.