Nonexistence and Non-Decoupling of the Dissipative Potential for Geo-Materials

Two fundamental issues exist in the damage theory of geo-materials based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.