A theoretical biomechanical acoustic framework for classifying dental restorative bilayers via Rayleigh-wave analysis

Predicting the acoustic response of coated elastic systems remains a challenging problem in nondestructive evaluation, particularly when interfacial mechanical contrast and layer thickness jointly govern complex dispersive behavior. In this work, generalized Rayleigh-wave propagation in dental restorative bilayer systems is theoretically investigated within a scanning acoustic microscopy framework. Four coating materials composite resin, amalgam, cobalt chromium alloy, and gold alloy are examined on glass-ionomer, silicate, and zinc-phosphate cement substrates. The Rayleigh critical angle and surface wave velocity are analyzed as functions of the normalized thickness h/λ T over the range 0-2. The results reveal two distinct propagation regimes separated at h/λ T ≈ 1. In the interaction-dominated regime, anomalous and non-monotonic dispersion emerges from strong layer-substrate mechanical coupling and is governed by a single dimensionless mismatch parameter ξ=(E L /E S )/(ρ L /ρ S ). In the asymptotic regime, dispersion vanishes as propagation becomes layer controlled. A four-type acoustic classification (Types A, B, C, D) is established from the joint analysis of ξ, the Anomaly Severity Index (ASI), and the Velocity Sensitivity Index (VSI), with a near unity linear ξ-VSI correlation (R 2 =0.98). The natural enamel-dentin bilayer (ξ=3.31, VSI=+79.8 %) is identified as the acoustic reference target for restorative design. These findings provide a unified and clinically actionable framework for evaluating acoustic compatibility in dental restorative assemblies.