Analysis of Acoustic Wave Propagation in Defective Concrete: Evolutionary Modeling, Energetic Coercivity, and Defect Classification

This study introduces a theoretical and computational framework for modeling acoustic wave propagation in defective concrete, with applications to non-destructive testing and structural health monitoring. The formulation is based on a coupled system of evolutionary hyperbolic equations, where internal defects are explicitly represented as localized energetic sources or sinks. A key contribution is the definition of acoercivity coefficient, which quantifies the energetic effect of defects and enables their classification as stabilizing, neutral, or dissipative. The model establishes a rigorous relationship between defect morphology, spatial distribution, and the global energetic stability of the material. Numerical simulations performed with an explicit finite-difference time-domain scheme confirm the theoretical predictions: the normalized total energy remains above 95% for stabilizing defects (𝜇𝑖>0 ), decreases by about 10% for quasi-neutral cases (𝜇𝑖≈0 ), and drops below 50% within 200μs for dissipative defects (𝜇𝑖<0 ). The proposed approach reproduces the attenuation and phase behavior of classical Biot-type and Kelvin–Voigt models with deviations below 5% while providing a richer energetic interpretation of local defect dynamics. Although primarily theoretical, this study establishes a physically consistent and quantitatively validated framework that supports the development of predictive ultrasonic indicators for the energetic classification of defects in concrete structures.