Investigation Of Coherent P/SV Waves In Random Composite Materials Using Fast Boundary Element Method

The random composite material is a kind of composites with uniformly randomly distributed inclusions.The coherent wave is an ensemble-averaged wave over different configurations of inclusions.The wave number of this coherent wave is a complex value,in which the real part represents the phase velocity of the coherent wave in the effective medium and the imaginary part means attenuation caused by multiple scattering.Estimation of attenuation of coherent waves in random composites is the theoretical basis for various applications of elastic wave in the fields of nondestructive evaluation of composites,geophysical exploration,noise reduction and vibration isolation.To date,accurate evaluation of the attenuation coefficient in term of theories,numerical simulations and experiments is still lacking,especially for cases of P-and SV-waves in composites with inclusions of complex shapes.In order to predict this parameter,a macroscopic model for the attenuation coefficient is proposed based on the physical mechanism of the attenuation caused by multiple scattering in composites.Then,large scale numerical simulations are conducted using the pre-corrected Fast Fourier Transform accelerated boundary element method(pFFT BEM)to specify the macro model.Based on the results of the numerical simulations,it turns out that the attenuation coefficient of coherent P-and SV-waves in random composites is a linear function of the total scattering cross section and number density of inclusions inside a unit area,with a coefficient of 0.556.The proposed macro model in this work has two advantages: one is that the formula is simple and easy to be used by engineers and technicians;the other one is that it has a clear physical meaning.In summary,the following three conclusions are obtained.First,when the volume fraction of inclusions is less than 4%,the macro model can be used to predict well the attenuation coefficient of P/SV waves.Second,when the volume fraction of inclusions is same,the macro works better for P-waves than SVwaves.Third,the proposed model is also applicable to cases with inclusions of complicated shapes.