On predicting elastic moduli and natural frequencies of multi‐phase composites with randomly distributed short fibers

Abstract This study presents a formulation to determine the overall stiffness of an n‐phase short fiber composite to include the inclusions' aspect ratio ranging from less than one to greater than one. The Mori‐Tanaka theory is initially employed to investigate the overall stress‐strain relation of a multi‐phase short‐fiber‐reinforced composite material, particularly whether or not the fibers and the matrix are isotropic, cubic, or transversely isotropic material. The effective stiffness tensor of a multi‐phase composite is then denoted as a function of the matrix's elastic moduli, the n‐phases' inclusions' elastic moduli, the n‐phases' inclusions' Eshelby tensor, and the n‐phases' inclusions' volume fractions. Utilizing the equivalent inclusion method allows us to model inclusions of n‐phases that consist of fictitious eigenstrains. In addition, the corresponding Eshelby tensors' values for ellipsoidal inclusion embedded in the isotropic matrix with the variation of aspect ratio are presented. Numerical results of the proposed formulation in solving a two‐phase composite closely correspond to the Halpin‐Tsai Equation. Results presented herein provide valuable information on the appropriate manufacturing requirements of multi‐phase composite materials or the design and optimization of multi‐phase composite structures.