Existing variational phase-field models for brittle fracture under multi-axial stress states face a critical limitation: they typically address either crack nucleation or unilateral contact behavior, but not both in a unified manner. Non-variational approaches, while capable of capturing these behaviors, often compromise the theoretical rigor inherent to the variational framework. To overcome this limitation, we propose a novel elastic strain energy decomposition scheme rooted in structured deformation theory. This decomposition enables the recovery of multi-axial failure surfaces corresponding to a wide range of phenomenological failure criteria, including the Rankine, Tresca, Mohr-Coulomb, von Mises, and Drucker-Prager types. Furthermore, it provides an accurate and consistent representation of complex crack kinematics—such as crack face contact and friction—with in a smeared continuum framework. A key contribution of our work is the derivation of a regularized residual strain energy formulation that replicates the mechanical behavior of sharp cracks while preserving thermodynamic consistency through the generalized standard materials framework. By explicitly incorporating the crack normal—prescribed according to a rule that relates its direction to the local principal stress directions via material-specific failure criteria—our approach defines the residual strain energy of fully disaggregated material at the representative volume element scale. This formulation naturally integrates crack orientation into the macroscopic strain kinematics, ensuring both physical fidelity and computational efficiency. By reconciling variational principles with material-specific strength criteria, the framework offers a unified, theoretically sound, and versatile tool for modelling fracture in brittle and cohesive-frictional materials. The model’s capabilities are demonstrated through numerical simulations that accurately predict crack nucleation stresses and orientations, while also capturing post-fracture contact and sliding behavior consistent with classical crack-face tractions during crack closure.