Cohesive phase-field fracture with an explicit strength surface: An eigenstrain-based return-mapping formulation

• Cohesive phase-field fracture with an explicit, tuneable strength surface. • Eigenstrains are updated by local return mapping at integration points. • Consistent tangents for smooth and non-smooth strength criteria are derived. • Formulation is implemented in a standard finite-element framework. • Benchmark cases show mesh-independence and phase-field length scale independence.