Nonlinear ultrasonic testing of concrete damage based on the stress–strain relationship of concrete hysteresis in non-classical nonlinear models

In the context of applying nonlinear ultrasonic detection to concrete damage, the nonlinear coefficients derived from theoretical models are of paramount importance. This study incorporates the nonclassical nonlinear hysteresis stress–strain relationship of concrete materials into the wave equation, combines boundary conditions, employs perturbation methods, and derives the hysteresis nonlinear coefficients δ₁ and δ₂. Considering the existing classical nonlinear coefficient β and the clapping nonlinear coefficient γ, nonlinear ultrasonic tests were conducted on pre-cracked concrete. Upon analysis of the test results, it was observed that the overall trends of the three nonlinear coefficients exhibited an increase with crack length and a decrease with crack angle. A comparison of the damage characterization performance of the three coefficients reveals that both the classical and the clapping nonlinear coefficient exhibit fluctuations during the damage changes. Whereas, the hysteresis nonlinear coefficients are capable of consistently representing the trend of damage evolution. The hysteresis nonlinear coefficients not only respond sensitively to changes in concrete damage but also clearly represent the changing trend of damage with minimal fluctuations and high robustness. Consequently, they are more suitable for damage detection in concrete materials. Furthermore, this conclusion is validated in both microcrack and multi-crack scenarios.