Stochastic discrete approaches for glass strength estimation

A numerical investigation on the load carrying capacity of a glass beam modelled as a material with a random strength distribution is presented. The strength values were distributed randomly within the beam by a Monte Carlo simulation, according to statistical distributions calibrated on experimental results obtained from literature. The elastic-plastic problem has been solved using two different computational discrete approaches implemented in two inhouse computer codes: a Rigid Body-Spring Model (RBSM) and a mesh-free numerical method arising from lattice-based Peridynamics. Being discrete approaches directly based on algebraic governing equations, they are suitable in problems involving brittle failure, because cracks are not viewed as a pathology of the displacement field. By providing an appropraiate mathematical and computational framework, the differences and analogies of these models are discussed and then the variability of the load capacity of the structural element is evaluated as a function of the statistics of the strength related to the size of the defects. The results obtained show that both RBSM and Peridynamics seem to be powerful tools for modelling the failure of brittle materials with heterogeneous strength properties.