A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks.

This paper presents a 3D homogenized model able to simulate the nonlinear effects generated by the interaction of ultrasonic waves with microcracks. A hexahedral element with one horizontal elliptical crack is constructed as a reference model. The reference model is smeared to be orthotropic but with different moduli in tension and compression to account for stiffness asymmetry due to crack opening and closure. Different from the existing homogenized models that usually simplify the representative volume element as a homogeneous part and require only one constitutive model for the equivalent material of the whole structure, we assign the constitutive relationship of the same reference model to all the finite elements but with random principal material orientations to take randomly oriented microcracks into consideration. In this way, the randomness of distributed microcracks can be considered in the framework of continuum mechanics. In this manner, the experimentally observed nonlinear effects, such as the generation of both even and odd harmonics, can be reproduced. The developed model has been verified for a 3D bar and a 3D plate. Particularly, the influence of crack density on the amplitude of higher harmonics is analyzed. [ABSTRACT FROM AUTHOR]