Numerical study of nonlinear elastic wave propagation in locally damaged engineering structures

Abstract

In this paper, the two-dimensional (2-D) ultrasonic wave propagation problem in an elastic half-space with a localized damaged zone is numerically simulated by a mapped Chebyshev pseudo-spectral collocation method [1]. The considered damaged zone, which is embedded in an undamaged host medium, is modelled by a nonlinear elastic and viscoelastic constitutive law. Classical nonlinear elastic and nonclassical hysteretic material behaviors are separately considered and evaluated. In particular, the classical nonlinear elasticity theory of Murnaghan [2] is implemented, while the hysteretic material behavior is modelled by the Duhem-model. To transfer the constitutive relations from the one-dimensional (1-D) to the 2-D case the Kelvin decomposition method is used. Furthermore, Convolutional Perfectly Matched Layers (CPML's) are used to simulate the semi-infinite elastic half-space. The computed time-domain signals are transformed to the frequency-domain and subsequently analyzed for different degrees of the wave attenuation and nonlinearity in the damage zone. The applications of the nonlinear ultrasonic technique are discussed based on the numerical results.