Theory of inverse problems for crack bridging stresses determination

A new mathematical procedure has been proposed for the determination of crack bridging stresses from perturbed crack opening displacements (COD) in fiber composites. The problem is an ill-posed inverse problem and the proposed procedure exploited concepts from functional analysis and the theory of inverse problems. The transformation from crack bridging stress into COD has been linearized, where the continuous crack bridging stresses functions of infinite dimensional vector spaces were approximated into finite dimensional subspaces. The coordinate representation of functions and the matrix of the transformation facilitated a numerical solution to the inverse problem. Self consistent direct and inverse problems were solved numerically in context to an example. Results establish that the proposed mathematical procedure produces fairly accurate results for engineering application.