Defect localization in fibre-reinforced composites by computing external volume forces from surface sensor measurements

We suggest a prospective method for detecting and visualizing defects in fibre-reinforced composites by computing external volume forces from measurements acquired by sensors that are integrated on the surface of the structure. Anisotropic materials like carbon fibre-reinforced composites are widely used in light weight construction which can exhibit damages that are not optically detectable. The key idea of our method is the interpretation of defects in such structures as if they were induced by an external volume force. This idea is based on the observation that a propagating elastic wave interferes with a damaged area by reflecting the wave. In that sense a damage can be seen as an additional source. Thus identifying the external volume force which has caused this wave is supposed to reveal the location of the defect. This approach leads to the inverse problem of determining the inhomogeneity of a hyperbolic initial-boundary value problem. We tackle this ill-posed problem by minimizing a Tikhonov functional which takes the oberservation points of our surface measurements into account. In the article we address the solvability of the direct problem, state and analyze the PDE-based optimization problem that aims for computing the external force and develop a numerical realization of its solution using the conjugate gradient method. First numerical results for a simple model case with different sensor adjustments show that the defects in fact are detectable. In that sense this article might be seen as starting point of future research which should comprehend deeper numerical studies and analysis of the problem. (paper)