Four-point combined DE/FE algorithm for brittle fracture analysis of laminated glass

A four-point combined DE/FE algorithm is proposed to constrain the rotation of a discrete element about its linked point and analyze the cracks propagation of laminated glass. In this approach, four linked points on a discrete element are combined with four nodes of the corresponding surface of a finite element. The penalty method is implemented to calculate the interface force between the two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The sequential procedure of brittle fracture is described by an extrinsic cohesive fracture model only in the DE subdomain. An averaged stress tensor for granular media, which is automatically symmetrical and invariant by translations, is used to an accurate calculation of the averaged stress of the DE. Two simple cases in the elastic range are given to certify the effectiveness of the combined algorithm and the averaged stress tensor by comparing with the finite element method and the mesh-size dependency of the combined algorithm and the cohesive model is also investigated. Finally, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with experimental results showing that the theory in this work can be used to predict some fracture characteristics of laminated glass.