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A variational formulation is proposed for a family of elastic–plastic–damage models within the framework of rate-independent materials. That consists first in defining the total energy which contains, in particular, a gradient damage term and a term which represents the plastic dissipation but depends also on damage. Then, the evolution law is deduced from the principles of irreversibility, stability and energy balance. Accordingly, the plastic dissipation term which appears both in the damage criterion and the plastic yield criterion plays an essential role in the damage–plasticity coupling. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses. A particular attention is paid on the equations which govern the formation of cohesive cracks where the displacement is discontinuous and the plasticity localizes. In the one-dimensional traction …