Models for wave propagation in two-dimensional random composites: A comparative study.

This paper provides a set of benchmark results on existing theoretical models for wave propagation in two-dimensional composite materials. This comparative study is motivated to investigate the reason why results from an accurate ultrasonic measurement often significantly contradict theoretical predictions. Eight different models are evaluated with their numerically calculated effective wave speeds and coherent attenuations. For computational simplicity, the problem of horizontal shear wave propagation in an elastic matrix containing parallel circular cylinders is considered. Numerical calculations are conducted for different composites in wide ranges of material properties, volume concentration, and frequency. Some of the numerical results are compared with experimental data. Judgments are made based on fundamental theoretical and physical criteria as well as relative agreements in the numerical results, and then possible causes of failures are discussed. The effect of microstructure, potentially as a major source of the observed disagreements between models, is also discussed.