Thermodynamically consistent nonlocal theory of ductile damage

In this paper a thermodynamically consistent, weakly nonlocal theory of ductile damage is presented. The theory is based on the classical dynamical balance laws of forces and couples in the physical space and dynamical balance laws of material forces on evolving defects and on the first and second law of thermodynamics formulated for physical and material space. Assuming general constitutive equations their frame-invariant and thermodynamically admissible form is determined. It is shown that physical and material forces and stresses consist of two parts, a nondissipative part derivable from a free energy potential, and a dissipative part, which can be obtained from a dissipation pseudo-potential, if such a pseudo-potential exists.The theory can be considered as a framework with gradient elastoplasticity, isotropic and anisotropic brittle and ductile gradient damage at finite strain as special cases.