Post-breakage in-plane stiffness of laminated glass. An engineering approach

In the post-breakage phase, laminated glass (LG) can maintain a residual load-bearing capacity due to the tension stiffening of the polymer through the adhesion with the shards, but the determination of the overall post-breakage stiffness presents formidable difficulties. A simple model is here proposed for the in-plane response of broken thermally treated LG, characterized by a fine cracking pattern. First, the delamination growth under both static and cyclic loading is numerically studied, by assuming a non-linear stress-separation law for the glass/interlayer interface. Then, homogenization techniques are used to derive a simple formula for the effective post-breakage stiffness under in-plane loading, which turns out to be dependent on interlayer modulus and amount of delamination. Comparisons with numerical experiments have evidenced the good accuracy of the formula, for different size and shape of both glass shard and delaminated region. The proposed model can be very useful in view of possible applications of LG as structural shear-resistant transparent diaphragms to be used, e.g., in the seismic retrofitting of historical monuments. Glass-based bracings should be designed to remain sound under moderate earthquakes, while breaking in a ductile manner and dissipate energy under the most severe events, due to the hysteretic response of broken LG.