A simple model for the post-breakage response of laminated glass under in-plane loading

Laminated glass, composed by glass plies bonded by polymeric interlayers, is used for structural purposes thanks to its safe post-glass-breakage response. When glass breaks, the shards remain attached to the interlayer, imparting to the damaged element a residual load-bearing capacity, influenced by the tension stiffening of the polymer through the adhesion with the glass shards and, hence, by the degree of delamination. The progression of delamination under cyclic loading has been studied numerically, by assuming a non-linear stress vs. separation law for the glass/interlayer interface. Using a micro-macro approach and homogenization techniques, energy theorems in linear elasticity provide a simple formula that furnishes a lower bound for the effective stiffness of heat-treated panels under in-plane loading, in particular under shear. Numerical experiments have been performed by considering glass shards with different sizes (varying from 20 mm to 100 mm) and shapes (square, rhombic and irregular quadrilateral), with amount of delamination ranging between 30% and 90%, with different shapes of the bonded zone (circular, square and rhombic with rounded corners). The results show that the proposed formula provides a good approximation of the effective stiffness, always on the safe side, with mean error of 6%. This study is of importance in view of the development of innovative glass-based bracings for the strengthening of buildings especially with respect to seismic events.