A regular triangular lattice mesh consisting of beam elements is adopted. The orientation of the mesh is chosen such that one of the beam directions corresponds to the direction of orthotropy of the material. Modelling of elastic and fracture orthotropy of the material is achieved by assigning lattice material properties depending on the beam orientation. The relations between the physical material properties and the fictitious lattice beam properties are derived analytically.

The model is then applied to a practical problem, i.e. the propagation of hydrostatic fracture in a brittle material subjected to compressive initial stresses. The initially stressed specimen is loaded by injection of a hydrostatic pressure inside a pre-existing notch. The load evolution and the direction of the progressive fracture are obtained for various levels of anisotropy and various boundary conditions. Valuable results are obtained for the prediction of the direction of fracture propagation.

In conclusion, the presented model proves to be an effective approach. Simulation of physically unstable fracture propagation, e.g. hydrostatic fracturing, can be achieved in a controlled and stable manner.

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