Calculation of Homogenized Mechanical Coefficients of Fiber-Reinforced Composite Using Finite Element Method

Abstract

Determining the mechanical properties of a composite material represents an important stage in its design and is generally a complicated operation. These values are influenced by the topology and geometry of the resulting composite and the values of the elastic constants of the components. Due to the importance of this subject and the increasing use of composite materials, different calculation methods have been developed over the last fifty years. Some of the methods are theoretical, with results that are difficult to apply in practice due to difficulties related to numerical calculation. In the current paper, using theoretical results offered by the homogenization theory, values of engineering elastic constants are obtained. The finite element method (FEM) is used to determine the stress and strain field required in these calculations; this is an extremely powerful and verified calculation tool for the case of a material with any type of structure and geometry. In order to minimize errors, the paper proposes the method of least squares, a mathematical method that provides the best estimate for the set of values obtained by calculating FEM. It is useful to consider as many load cases as possible to obtain the best estimates. The elastic constants for a transversely isotropic material (composite reinforced with cylindrical fibers) are thus determined for a real case.