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The problem of propagation of interfacial failure in patched panels subjected to temperature change and transverse pressure is formulated from first principles as a propagating boundaries problem in the calculus of variations. This is done for both cylindrical and flat structures simultaneously. An appropriate geometrically nonlinear thin structure theory is incorporated for each of the primitive structures (base panel and patch) individually. The variational principle yields the constitutive equations of the composite structure within the patched region and an adjacent contact zone, the corresponding equations of motion within each region of the structure, and the associated matching and boundary conditions for the structure. In addition, the transversality conditions associated with the propagating boundaries of the contact zone and bond zone are obtained directly, the latter giving rise to the energy release rates in self-consistent functional form for configurations in which a contact zone is present as well as when it is absent. A structural scale decomposition of the energy release rates is established by advancing the decomposition introduced in W. J. Bottega, Int. J. Fract. 122 (2003), 89-100, to include the effects of temperature. The formulation is utilized to examine the behavior of several representative structures and loadings. These include debonding of unfettered patched structures subjected to temperature change, the effects of temperature on the detachment of beam-plates and arch-shells subjected to three-point loading, and the influence of temperature on damage propagation in patched beam-plates, with both hinged-free and clamped-free support conditions, subjected to transverse pressure. Numerical simulations based on closed form analytical solutions reveal critical phenomena and features of the evolving composite structure. It is shown that temperature change significantly influences critical behavior.

The coupling of edge debonding and thermal buckling of patched beam-plates possessing initial edge detachment is examined for the case when the structure is subjected to a uniform temperature change. The geometrically nonlinear analytical model employed is that established by the authors in a prior work. The problem is recast in a mixed formulation in terms of the transverse deflection and the membrane force to aid in the analysis and physical interpretation. The interaction of edge-debond propagation and thermal buckling is studied. The phenomenon of buckle-trapping, originally obseii'ed by the authors in a congruent study, as well as the phenomenon of sling-shot buckling, is seen to manifest itself in the debonding behavior. The evolution of the structure is predicted as a function of given material and geometric parameters from numerical simulations based on analytical solutions of the nonlinear problem. A (propagating) contact zone adjacent to the bonded region is accounted for, and its presence or absence, as well as its nature, is seen to be highly influential in the global as well as local behavior of the structure.

The problem of edge debonding of patched beam-plates subjected to transverse pressure is examined using two related mathematical models; one which incorporates geometric nonlinearities and the other which neglects them. The models, developed in a prior study, present the energy release rates in self-consistent functional form and yield closed form analytical solutions for the specific problem of interest. Results of numerical simulations based on each model are presented in the form of debond growth paths and compared. The growth paths are subsequently presented with corresponding pre-growth load-deflection paths to further examine the differences resulting from each model. It is seen that significant discrepancies occur between the behaviors predicted by the two models, both with regard to the onset of damage propagation and with regard to the stability of the process, as well as with regard to the pre-growth behavior, demonstrating the critical influence of geometric nonlinearities on the phenomena of interest.

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