Estimating Effective Material Parameters of Inhomogeneous Layers Using Finite Element Method

Abstract

This study presents a finite element method (FEM) approach to estimate the effective medium parameters of 2-D and 3-D layers of arbitrary composition. The resonance frequency of a layer to be investigated is found by exciting the layer with plane waves and studying the reflected sound pressure from the layer as a function of frequency and incidence angle. This allowed for the calculation of compressional and shear wave velocities. The method was validated by applying the method to layers with known acoustic parameters and by comparing with results from the established analytical models. Composite layers with 1-3 and 2-2 connectivity are well described by established effective-medium theories, but these require the composite structures to be small compared to the acoustic wavelength. This limitation was overcome by the described FEM-based model, which could also capture deviations occurring in coarser composites. Conventional analytical models predict wave velocities as a function of void concentration, not considering positions of the voids. The described FEM approach predicted up to 5% variation in wave velocities for gold layers with identical volume fraction of voids, depending on the void distribution. This demonstrates that void positions influence wave velocity. The influence of connectivity between inclusions was studied by modeling tungsten inclusions in an epoxy matrix. It was found that composites with inclusions connected in a preferred direction had higher wave velocity in the direction of connectivity compared to randomly oriented inclusions. It is concluded that the presented FEM model reproduces the literature values for homogeneous materials and agrees with effective medium theories for fine-pitched composites. However, the strength of the model is its ability to go beyond this and model phenomena in real finite-size composites not captured by the classic effective medium models.