Phase-field modelling of fracture is gaining popularity in the fracture mechanics community, particularly for its ability to generate cracks with arbitrarily complex geometries and topologies in two and three dimensions without the need for ad hoc criteria. The model first introduced in [1] has a clear connection with Griffith’s propagation criterion via Gamma convergence tools and recent results [2] have shown that, in addition to propagation, it can quantitatively predict crack nucleation for mode-I loading. However, the initial model cannot reproduce with flexibility the experimentally measured strengths under multiaxial loads. Moreover, a modification is necessary to avoid the interpenetration of crack surfaces in compression and reflect the physical asymmetry of fracture behaviour between tension and compression [3]. In this presentation, staying within the realm of variational approaches, we discuss existing modifications based on energy decomposition, their shortcomings, and the requirements for an effective energy decomposition method to model crack nucleation and propagation. Finally, we introduce a new energy decomposition, the star-convex model, that solves (at least partially) the issues with the existing ones [4]. REFERENCES [1] B. Bourdin, G. A. Francfort and J. J. Marigo, Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids 48 (2000) 797–826. [2] E. Tanné, T. Li, B. Bourdin, J. J. Marigo and C. Maurini. Crack nucleation in variational phase-field models of brittle fracture. Journal of the Mechanics and Physics of Solids 110 (2018) 80–99. [3] H. Amor, J. J. Marigo and C. Maurini. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. Journal of the Mechanics and Physics of Solids 57 (2009) 1209–1229. [4] F Vicentini, C Zolesi, P Carrara, C Maurini, L de Lorenzis. On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states. Preprint (2023): hal-04231075.