Analytic Solutions for Clamped Nonlinear Mindlin Plates to Predict Sandwich Structure Debonding

Unvented honeycomb sandwich structures are used in many space and aeronautical applications. During atmospheric ascent, pressure differentials can build up within the sandwich core, causing facesheet-core debonding. Engineers often predict debonding using the Virtual Crack Closure Technique (VCCT) which requires detailed finite element analysis. These VCCT simulations are expensive, due to geometric nonlinearity and explicit modeling and propagation of the crack interface. In this context, analytic solutions are valuable throughout the structural design process. In conventional debond solutions, the facesheet is modeled as a metal Kirchoff circular plate with clamped edges, omitting transverse shear and orthotropic effects. Even for pure bending, existing clamped plate solutions are limited, with only a single term solution for nonlinear Kirchoff theory, and no solution for nonlinear Mindlin theory. To address this gap, we develop novel series solutions for clamped nonlinear Kirchoff and clamped nonlinear Mindlin plates, including composite materials and a unidirectional in-plane load. We derive a solution for the total energy release rate of facesheet debonding. Our propsed Mindlin solution uses a conservative mode shape, but is still within 8% of the energy release rate for large deflections. For square plates, we find that a a single term in the series gives adequate accuracy, but extra terms are needed at high aspect ratios.