Fracture mechanics is nowadays a consolidated theory within the realm of continuum mechanics, that has been developed starting from the pioneering work of Griffith [1], where the key concepts of energy release rate and fracture toughness (surface energy) have been established. A remarkable variational extension of such a theory has been proposed by Francfort and Marigo [2]. A lacking feature of Griffith’s fracture criterion, including its variational extensions, is the inability to capture and describe fatigue cracks, that is cracks evolving due to repeated loads that individually would be too small to cause material failure. In this contribution, we will propose a phenomenological model that endows Griffith’s fracture criterion with the ability to describe fatigue cracks. The key idea of the present model is to consider the fracture toughness not as a material parameter anymore but rather as a material function, assumed to decrease as an accumulated energy based measure increases [3]. Analytical and numerical examples will shown the capability of the present model to recover Paris fatigue law and many other key features of fatigue crack propagation. REFERENCES [1] Griffith, A. A. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London, Vol. A221, pp. 163-198, 1921. [2] Francfort, G. A. and Marigo, J. J. Revisiting brittle fracture as an energy minimization problem. Journal of the Mechanics and Physics of Solids, Vol. 46(8), pp. 1319-1342, 1998. [3] Alessi, R. and Ulloa, J. Endowing Griffith’s fracture theory with the ability to describe fatigue cracks. Engineering Fracture Mechanics, Vol. 281, 109048, 2023.