Evaluating the elastic wave speed in heterogeneous materials and structures: A concurrent multiscale modeling approach

Elastic wave speed is significant for studying materials’ dynamic behavior, and usually evaluated using the classical equations c=E/ρ or c=λ+2μ/ρ especially for homogeneous isotropic materials. However, these analytical methods may not be suitable for heterogeneous materials and structures, while the direct numerical simulation (DNS) using finite element method requires a huge number of elements which leads to unmanageable computational cost. To this end, the Direct Finite Element Square (DFE²) method was used to simulate the elastic wave propagation in heterogeneous materials and structures, whereby it was proposed that both meso-scale stress and density should be scaled in the DFE² method to accurately predict the wave transmission time in heterogeneous materials. Also, it was found that DFE² method generally predicts a higher elastic wave speed due to the unrealistic wave transmission in the macro-element at the impact end, and the error can be reduced by refining the macro-elements. Simulation of several heterogenous materials such as fiber reinforced polymer composites, anisotropic cellular structures and density-gradient porous panels show that the DFE² method can capture the elastic wave speed in 2D heterogeneous materials and structures more accurately compared to classical estimation equations, whereby the DNS result was used as reference. Moreover, the DFE² method exhibits a high computational efficiency, i.e., more than 10 times higher than DNS, and can be easily implemented using available features in commercial software. This implies the valuable potential of the DFE² method in evaluating the elastic wave speed in heterogeneous materials and structures.