An element-based homogenized model for nonlinear wave interaction with 2D distributed microcracks

Interests in using nonlinear acoustic methods for incipient damage detection continue to grow tremendously as the understanding of nonlinearities in micro-cracked and cracked solids. It is widely known that nonlinear effects caused by cracks are stronger than crack-induced linear phenomena. However, understanding physical mechanisms related to various nonlinearities still needs to be clarified, which is vital to implementing nonlinear ultrasonics for engineering applications. To this end, an element-based homogenized method is proposed, which can consider the randomness of distributed microcracks in the framework of continuum mechanics. A quadrilateral element with one horizontal crack is constructed as a reference model. The reference model is homogenized to be orthotropic but with different moduli in tension and compression to account for stiffness asymmetric due to crack opening and closing. Unlike the existing homogenized method, which usually simplifies the representative volume element as a homogeneous part and requires 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 directions to take randomly oriented microcracks into consideration. The proposed method is compared with the finite element contact model that defines contact properties on crack surfaces. It is validated that the proposed method agrees well with the contact model for simulating the nonlinearities in wave interaction with the microcracks but at a much lower computational cost.