One of the main contemporary challenges facing engineering sciences is how to identify the actual state of internal defects, their self-organized criticality, interaction, and thus influence on the overall strength and durability of a system. In this study we address one aspect in the panoply of problems emerging in this context, namely: how to identify a single delamination in a layered composite specimen performing measurements only on the surface. In rigor terms the answer to this question relates to the answer to the question of how to solve the nonlinear semi-inverse problem of the mathematical programming emerging from the minimization of an associated Kohn-Vogelius functional with respect to some set of design variables parameterizing the delamination region. Clearly, one methodological way to approach the solution is to use some classical, gradient-based, nonlinear programming technique, like SQP. One should not forget, however, that the identification problems of this class are per se ill-posed, nonsmooth, and highly sensitive to the initial boundary data. Three bottlenecks occur that cannot be trivially circumvented when the shape of the delamination region, its characteristic dimensions, and position are preliminarily unknown (or highly uncertain). Based on an appropriate split of the governing Kohn-Vogelius functional we succeed here in transforming the ill-posed local inverse problem into a coupled system of elliptic well-posed Euler-Lagrange equations and to derive a direct smooth iterative strategy for its numerical solution. The strategy leads to a semiempirical reconstruction method for finding isolated interlaminar cavities from the measurement of the displacement field performed on the surface of the specimen.
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