Ryzhkov O. Propagation of nonlinear elastic waves in periodicallyheterogeneous composite materials

The higher-order asymptotic homogenization method is developed. The macroscopic wave equations describing the propagation of elastic strain waves in layered and fibrous composite materials are obtained. The effects of nonlinearity (geometrical, physical, structural) and dispersion are taken into account. Approximate analytical solutions for the effective elastic coefficients are derived. An estimation of the area of applicability of the obtained homogenized models is proposed. The analytical solutions for stationary waves in layered and fibrous materials are obtained. A pseudo-spectral numerical procedure for the integration of nonlinear wave equations is developed. The numerical simulation of non-stationary waves in a layered material is performed. The conditions for the formation of localised nonlinear waves are determined. The obtained results can be applied to facilitate the development of new methods of acoustic diagnostic and to predict the dynamic failure of heterogeneous materials and structures.