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We analyze the applicability of a modified Leonov-Panasyuk-Dugdale model to the description of the propagation of a mode I crack in structured materials under plane stress conditions. For quasi-brittle materials, refined formulas of the critical length of the prefracture zone and the critical load containing a structural parameter are proposed. The Kornev model is extended to the case of quasi-ductile materials. Numerical simulation of plastic zones in square plates of a bimetal and a homogeneous material under quasi-static loading is performed. In the numerical model, the equations of deformable solid mechanics are expressed in the Lagrangian formulation, which is the most preferred for large-strain deformations of elastoplastic materials. The results of the numerical experiments are consistent with the results of calculations using the analytical model for the fracture of structured materials.