## 7 Conclusions  
The outcome of this study is the quantification of precursors to damage using hybrid nonlocal micro-continuum mechanics in the piezoelectric anisotropic sensors. The incubation of damage at the micro scale acts as a precursor to the macro-scale effect, which is an indicator for prognosis of the damage. In this study, a micro-scale surface crack of 0.2 \(\upmu\)m depth is quantified using the proposed formulation. An intrinsic length scale parameter obtained from nonlocal micro-continuum mechanics is evaluated and used as an indicator of precursors to damage. The experimental investigations were performed to detect damage in a LiNbO\({}_{3}\) crystal using IDT sensors and scanning acoustic microscopy. The manifestation of surface flaws upon characteristic changes in SAWs and longitudinal bulk wave propagations were investigated for damage detection. The changes in TOF and frequency content of the surface acoustic waves and bulk waves are studied for the detection and quantification of the damage. In order to quantify the manifestation of surface defects on the waves characteristic, the explicit expressions of the wave dispersion in anisotropic piezoelectric sensors are derived. The dispersion relationship for the anisotropic solid is derived using Christoffel equations, which incorporate the effect of intrinsic length scale parameters at micro scale. Based on the nonlocal elastic kernel theory, angular dispersion relationships are plotted for longitudinal, fast and slow transversal wave velocities considering the piezo stiffening in piezoelectric crystal. The study evaluates experimental changes in speed of sound and frequency shift of SAWs and longitudinal waves and is overlaid on theoretical dispersion curves. The reference state of the piezoelectric sensors is considered to have intrinsic length scale parameter \(e=0\). The damage initiation and evolution in sensors is quantified using the nonlocal parameter with respect to the reference state. All of the results presented in this study are summarized in Table 1. The speed of the longitudinal and transversal waves in the reference state (\(e=0\)) is evaluated as 7692 m/s and 3571 m/s, respectively. Due to the presence of the micro-crack on the surface of the LiNbO\({}_{3}\) crystal, the speed of longitudinal and transversal waves is determined as 6666 m/s and 3455 m/s, respectively. Instead of determining the exact depth of the micro-crack, we envisage quantifying the magnitude of severity of the damage using the nonlocal damage parameter. The influence of the severity of damage on longitudinal waves is quantified using nonlocal parameter \(\Delta e_{ls}^{piezo}=0.6\). Similarly, the nonlocal parameter of \(\Delta e_{ls}^{piezo}=0.6\) was quantified depicting the influence of damage on transversal wave propagation. The relative change in magnitude of nonlocal parameter reflects the manifestation of severity of damage. **Author Contributions:** [PERSON] and [PERSON] has implemented the nonlocal micro-continuum mechanics algorithms. [PERSON] conceptualized, designed, and fabricated the sensor. U.A. provide the valuable support during all the experiments. [PERSON] and [PERSON] wrote the original draft, reviewing, and editing the manuscript with support from all co-authors. [PERSON], [PERSON] and U.P. supervised the experiments and numerical analysis of the paper and provided valuable inputs in manuscript preparation. Funding was secured by U.P., S.B. and A.H.  
**Funding:** The project is partially funded by Skoltech and the office of Vice President of Research at the University of South Carolina. [PERSON] and [PERSON] are great to [PERSON], Universitario de Cantoblanco, for his mentorship. [PERSON] and [PERSON] gratefully acknowledge the support provided by The Research Council of Norway and Norwegian Micro-and Nano-Fabrication Facility, NorFab. The publication charges for this article have been funded by a grant from the publication fund of UiT The Arctic University of Norway.