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Crack growth in non-linear quasi-brittle materials is addressed by a new approach. This approach is
consistent with the Linear Elastic Fracture Mechanics framework ; the velocity field around the crack tip is
represented by a sum of shape functions and their intensity factors. However, the LEFM kinematics is enriched
to account for the non-linear behaviour of the material. Additional shape functions and their intensity factors
are used to capture the effect of the nucleation of micro-cracks on the crack tip fields. So as to construct these
shape functions, a multi-scale approach is employed. The discrete element method is used to compute the
velocity field around a crack tip with boundary conditions extracted from finite element simulations. The results
are post-treated using a proper orthogonal decomposition to generate additional shape functions for mode I
and mode II loading conditions. Once this is done, the evolution of crack tip damage during a complex loading
scheme is condensed into the evolutions of the intensity factors of the two additional shape functions.