The main objective of this report is to compute the energy balance for the modelling of fractures in 2D materials using Phase-fields models as a tool to verify the results. For a civil engineer, it is important to compute the resistance of materials as fractures are responsible of structures failures. The strategy is to use an adaptive refinement method for phase-fields models developed by A.Muixí and to study how the spatial and temporal characteristics of the model affects the balance. The energy balance is composed as the sum of the elastic and brittle fracture or crack energy, the total energy is calculated as the work of the external forces using Newton-Cotes methods to compute it. For the elastic energy and crack energy, the weak form and discretization methods were applied to solve PDEs and to compute volume integrals. The analysis of the results of the energy balance, shows that the balance can adapt to complex geometries with discontinuities or cyclic loading cases. The crack length and the balance error can be indeed used as a tool to verify if the precision of the model numeric parameters is enough. The parameters studied are the temporal and spatial discretization and the tolerance of the non-linear iterative solution of the damage. Although the results found are satisfactory, an error appears when the crack propagation speed is important product of the kinetic energy not taken into account in the balance. As the velocity of propagation is relatively slow at the loading phase, the kinetic energy can be ignored and the obtained balance is correct. For an analysis post-failure this thesis proposes a dynamic approach of the hybrid phase-field model taking into account the inertia