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• A full 3-D analytical model for interpreting nonlinear aspects of guided ultrasonic waves modulated by a fatigue crack of "breathing" behavior. • An analytical insight into the generation of contact acoustic nonlinearity from fatigue crack. • A nonlinearity index for quantitatively evaluating fatigue crack including crack length. • A capacity of predicting initiation of a fatigue crack at an embryonic stage. • Rigorous experimental validation and numerical validation. Previously, a two-dimensional (2-D) analytical model for interpreting the modulation mechanism of a "breathing" crack on guided ultrasonic waves (GUWs) is developed [1]. Based on the theory of wave propagation in three-dimensional (3-D) waveguides and using an elastodynamic analysis, the 2-D model is extended to a 3-D regime, to shed light on the nonlinear aspects of GUWs disturbed by cracks with "breathing" traits. With the model, generation of contact acoustic nonlinearity (CAN) embodied in GUWs, subjected to the key parameters of a "breathing" crack (e.g., crack length), is scrutinized quantitatively. On this basis, a nonlinearity index is defined to link crack parameters to the quantity of extracted CAN. In virtue of the index, initiation of an undersized fatigue crack in a 3-D waveguide can be delineated at its embryonic stage, and, in particular, the crack severity can be quantitatively depicted. This facilitates prognosis of imminent failure of the monitored structure. Experimental validation is performed in which a hairline fatigue crack is evaluated, and the results well corroborate the crack parameters predicted by the 3-D analytical model. [ABSTRACT FROM AUTHOR]

• First enriched finite element for general wave propagation problems in piezoelastic media. • First element to accurately predict electroelastic, narrowband guided waves to broadband impact waves. • Results show the need of enriching both displacement and electric potential fields. • Accurately captures free edge stress field with steep gradients at piezoelectric actuator-structure interface. • Exhibits much greater computational efficiency, accuracy and faster convergence than conventional FE. A two dimensional finite element (FE) is developed by enriching the conventional Lagrange interpolation functions with local element domain wave functions, for accurate solution of general wave propagation problems in piezoelastic media. The enrichment functions, applied to both displacement and electric potential fields, satisfy the partition of unity condition, and vanish at the nodes. The formulation is developed using the extended Hamilton's principle for piezoelastic solids, considering two-way electromechanical coupling. The enriched FE is shown to perform equally well in terms of computational efficiency and accuracy for broadband impact induced electroelastic wave to narrowband ultrasonic guided wave propagation problems, unlike the other available elements. The solution for impact in a piezoelectric plate is shown to alleviate the spurious undulations in both velocity and electric potential fields, which are encountered in the conventional FE solutions. For the problem of high frequency Lamb wave actuation and sensing in a thin plate bonded with piezoelectric actuator/sensor patches, the element shows significant improvement in the computational efficiency over the conventional FE. Further, the free edge effect of steep gradients in the shear stress distribution at the actuator-plate interface is accurately captured by the proposed element using much fewer degrees of freedom than the conventional FE. [ABSTRACT FROM AUTHOR]