Real-time imaging of interfacial damage in layered composites

TL;DR

This paper introduces a non-iterative, high-resolution imaging method for detecting and characterizing interfacial fractures in layered composites using elastic-wave sensing and an adapted $F_ atural$-factorization approach.

Contribution

It develops a novel, convex, FM-based imaging functional for real-time, non-iterative detection of interfacial damage in heterogeneous layered composites.

Findings

High spatial resolution in fracture imaging.

Robustness to measurement errors and uncertain elasticity.

Fast, non-iterative data inversion process.

Abstract

A theoretical platform is developed for active elastic-wave sensing of (stationary and advancing) fractures along bi-material interfaces in layered composites. Damaged contact surfaces are characterized by a heterogeneous distribution of (elastic) stiffness $\boldsymbol{K}$ which is a-priori unknown. The proposed imaging functional takes advantage of sequential wavefield measurements for non-iterative and concurrent reconstruction of multiple fractures in heterogeneous domains, with an exceptional spatial resolution and with minimal sensitivity to measurement errors and uncertain elasticity of damage zones. This is accomplished through adaptation of the $F_\sharp$-factorization method (FM) applied to elastodynamic wavefields in a sensing sequence i.e. a measurement campaign performed before and after the formation (or evolution) of interfacial fractures. The direct scattering problem is formulated in the frequency domain where the damage support is illuminated by a set of incident P- and S-waves, and thus-induced scattered waves are monitored at the far field. In this setting, the germane mixed reciprocity principle is introduced, and $F_\sharp$-factorization of the differential scattering operator is rigorously established for composite backgrounds. These results lead to the development of an FM-based fracture indicator whose affiliated cost functional is inherently convex, thus, its minimizer can be computed without iterations. This attribute coupled with the reduced sampling space, proposed in this work, remarkably expedite the data inversion process. The performance of proposed imaging functional is demonstrated by a set of numerical experiments.