https://doi.org/10.1140/epjp/s13360-025-06800-4
Regular Article
Wave scattering and dynamic stress concentration in piezoelectric half-planes with semi-elliptical notches under SH-wave excitation
1
Department of Management, College of Business Administration, Princess Nourah Bint Abdulrahman University, P.O.Box 84428, 11671, Riyadh, Saudi Arabia
2
Department of Mathematics, College of Science, Qassim University, 51452, Buraydah, Saudi Arabia
3
Christ University, 560029, Bengaluru, India
Received:
13
February
2025
Accepted:
27
August
2025
Published online:
8
September
2025
This study presents a comprehensive analytical framework for investigating the scattering and dynamic stress response of semi-elliptical notches in piezoelectric half-planes subjected to anti-plane shear (SH) waves. The primary objective is to unify the treatment of notches, cracks, and circular holes within a rigorous wave–defect interaction model while explicitly incorporating piezoelectric coupling and nanoscale surface/interface effects. The methodology employs the complex function method in conjunction with the Helmholtz equation and wavefield superposition theory, leading to an infinite system of equations that rigorously satisfies continuity and boundary conditions; a systematic truncation strategy is then applied to achieve convergent solutions. Results demonstrate that surface/interface effects significantly suppress the dynamic stress concentration factor, particularly under vertical SH-wave disturbance, while resonance peaks become sharper at low modulus ratios and higher piezoelectric constants such as PZT-5H and BaTiO3. Importantly, the formulation naturally recovers classical elasticity results in the absence of piezoelectric effects, providing strong theoretical consistency. Validation is achieved through analytical recovery of benchmark cases (semicircular notch and edge crack), graphical comparisons with established results, and rapid convergence of the truncated system, confirming both accuracy and robustness. The practical implications of these findings extend to structural health monitoring, non-destructive evaluation, and the optimal design of advanced piezoelectric composites, where accurate prediction of defect evolution and stress amplification is critical. While the present work is restricted to semi-elliptical notches under SH-wave excitation in half-plane geometries, the approach is readily extensible to more general defect shapes and mixed-mode disturbances. The novelty of this study lies in its ability to capture piezoelectric surface/interface effects within an exact analytical framework, providing predictive capability for defect-induced stress concentrations and offering a reliable basis for the design and reliability assessment of high-performance piezoelectric materials.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
