High-order nonlinear contact effects in cyclic loading of delaminated sandwich panels

The interaction between the delaminated surfaces and its influence on the static and on a special type of cyclic load behavior of delaminated sandwich panels is studied. In addition, the results for a cyclic push–pull load and the analysis for the detection of damage in sandwich panels is presented. The analysis uses the high-order theory of sandwich panels (HSAPT) and considers geometrical nonlinear effects and the nonlinearity associated with the contact characteristics of the delaminated surfaces. The nonlinear contact phenomena, which are associated with variation of the contact conditions during motion, result in differences in the stiffness of the delaminated panel, which are detected under a push or pull type of loads. Quantitative assessment of these differences sheds light on the existence, size, and location of the delaminated region and can be used for a nondestructive evaluation of the damage characteristics of the delaminated panel. The field equations and the corresponding boundary and continuity conditions of the nonlinear analytical model are derived via the variational principle of virtual work. The mathematical formulation uses the ordinary unidirectional panel theory for the face-sheets and a two-dimensional elasticity approach for the core. It yields a set of nonlinear differential equations that are solved using the Multiple Shooting Method combined with a Newton–Raphson iterative scheme. The influence of the nonlinear contact phenomena on the behavior of the panel under two loading schemes is numerically studied. The first loading scheme is a push–pull loading simulation that demonstrates the concept of the proposed damage detection method. The second loading scheme simulates the conditions that evolve during free vibration response. The results reveal the role of the nonlinear contact phenomena in the cyclic bending behavior of the sandwich panel and its influence on the localized and overall nonlinear response. A summary and conclusions close the paper.