The Quick Determination of a Fibrous Composite’s Axial Young’s Modulus via the FEM

Knowing the mechanical properties of fiber-reinforced composite materials, which are currently widely used in various industrial branches, represents a major objective for designers. This happens when new materials are used that are not yet in production or for which the manufacturer cannot give values. Given the practical importance of this problem, several methods of determining these properties have been proposed, but most of them are laborious and require a long calculation time. And, some of the proposed calculation methods are very approximate, providing only upper and lower limits for these values. Experimental measurements are obviously the optimal solution for solving this problem, but it must be taken into account that this type of method consumes time and material resources. This paper proposes a sufficiently accurate and fast estimation method for determining Young’s modulus for a homogenized fibrous material. Thus, the FEM is used to determine the natural frequencies of a standard bar, for which there are sufficiently precise classical methods to express the engineering constants according to the mechanical properties of the component phases of the homogenized material. In this paper, Young’s modulus is determined for such a material using the relationships that provide the eigenfrequencies for the longitudinal vibrations. With the adopted model, transverse and torsional vibrations are eliminated by blocking the nodes on the surfaces of the bars. In this way, more longitudinal eigenfrequencies can be obtained, so the precision in calculating Young’s modulus is increased.