Abstract: Based on the concept of thermodynamics, two fundamental constitutive issues in the thermodynamics theory of damage-elasto-plasticity are proposed: first, existence or inexistence of the dissipative potential; second, the dissipation potential can or cannot be decomposed into a damage potential and a plasticity potential, namely, whether or not the two mechanisms can be decoupling. Within this framework, sufficient and necessary conditions for the existence and the coupling of a dissipation potential are given under total and increment forms, and it proves the sufficient and necessary conditions strictly in theory. According to the mechanical properties of the geo-materials, the inexistence and the un-decoupling of the dissipation potential are also proved.