Numerical modeling of wave propagation in a cracked solid

Abstract

In this study, we investigate the dynamics of (damaged) materials with a nonlinear microstructure (microcracks in frictional contact) using a discontinuous Galerkin method. Although the propagation of a plane wave is associated with a complex phenomenon and the stress field loses its homogeneity, the loading pulse has an overall front wave at each moment. Thus, a macroscopic behavior can be extracted and compared with reference solutions based on analytical formulas deduced from the effective (static) elasticity models of a cracked solid. The influences of the mesh and of the microcrack pattern have been tested to choose an optimal numerical setting. We analyzed the sensitivity of the damaged pulse with respect to microcrack density, wavelength, and microcrack orientation. For small values of crack density parameter, the theoretical formula and the computed speed of the damaged pulse are very close, but for larger values there is an important gap between them. For large ratios of wavelength over crack length, the wave speed depends only on the crack density parameter. However, if this ratio is of the order of unity, the wave speed, pulse duration, and pulse amplitude are very sensitive to the wavelength. For more complex phenomena, namely blast propagation in a cracked material, we discuss how the microcrack orientation affects wave propagation and scattering.