# Elastic Constants of Polymeric Fiber Composite Estimation Using Finite Element Method

## TL;DR

This paper introduces a fast method using FEM to estimate elastic constants of polymeric fiber composites by analyzing beam vibrations.

## Contribution

A novel FEM-based approach for quickly estimating homogenized elastic constants of composite materials.

## Key findings

- Eigenfrequencies of beam specimens are computed using FEM to estimate homogenized material constants.
- The method considers both phases of the composite with accurate geometry and real size.
- The approach is demonstrated for a fiber-reinforced polymer composite material.

## Abstract

Determining the properties of composite materials (knowing the properties of the component phases) is a primary objective in the design phase. Numerous methods have been developed to determine the elastic constants of a composite material. All these methods are laborious and require significant computing time. It is possible to make experimental measurements, but these too are expensive and time-consuming. In order to have a quick estimate of the value of the engineering constants of a new composite material (in our study a polymeric matrix reinforced with carbon fibers), this paper proposes a quick method for determining the homogenized material constants, using the finite element method (FEM). For this, the eigenfrequencies of a beam specimen manufactured by the studied composite material will be computed using FEM. The model will consider both phases of the composite, with the geometry and real size. The mechanical properties of the constituent’s material phases are known. With the help of this model, the torsional, longitudinal and transverse vibrations of the beam are studied. Based on the eigenvalues obtained by this calculation, it now is possible to quickly estimate the values of homogenized material constants required in the design. An example for a fiber-reinforced polymer composite material is provided in the paper.