Determination of dynamic effective properties in functionally graded materials

Summary This work is dedicated to the investigation of the dynamic effective properties in functionally graded materials resulting from an anti-plane shear wave. A micromechanics-based elastodynamic model is developed to predict the dynamic behavior of two-phase functionally graded materials, and the distribution of dynamic effective properties in the gradation direction is presented. Generally speaking, in functionally graded materials there exist two microstructurally distinct zones: a fiber-matrix zone and a transition zone. In the fiber-matrix zone, the dispersion relation for the effective wave number is derived using the effective medium method, and the dynamic effective properties for any macroscopic material points are determined in the corresponding microstructural representative volume element (RVE). In the transition zone, a transition function is introduced to make the wave fields continuous and differentiable. Numerical examples of the dynamic effective properties in the gradation direction under different parameters are presented graphically. The obtained results reveal that the distribution of dynamic effective properties in the gradation direction is dependent on the material properties of each phase, the incident frequency, and the gradation parameter of the materials. Comparisons between numerical solutions and experimental data are also made. At last, the results are discussed in detail.