Continuous and lattice models to describe crack paths in brittle–matrix composites with random and unidirectional fibres

Two computational models for the simulation of the cracking behaviour of fibre-reinforced brittle–matrix composites – based on a continuous finite element (FE) approach and on a lattice approach, respectively – are presented. Such a class of materials is characterized, in the case of aligned fibres, by a high level of anisotropy due to the preferred fibre orientation in the bulk material. The main mechanical aspects being involved, such as crack appearance, crack propagation, fibre bridging effects, fibre debonding and breaking can be taken into account by the presented models. The advantages and drawbacks of the above approaches are outlined through some applications related to plain and fibre-reinforced brittle materials under both Mode I and Mode I + II loading. The numerical findings emphasize that the lattice approach allows us to describe in detail the crack pattern at microscale level, whereas the continuous FE approach allows us to perform computationally economic analyses yielding overall information of the mechanical problem.