Gradient theories of ductile and brittle damage: A thermodynamical consistent framework and computational issues

Abstract

The aim of this chapter is to derive a thermodynamically consistent gradient-damage theory for ductile and brittle damage. It is assumed that evolving microdefects have inertia and that their motion is caused by microforces that have to satisfy their own dynamical balance laws. In addition to the balance laws of macro and microforces, the chapter formulates the first and second law of thermodynamics for macro and meso levels. Assuming the constitutive equations in general form, it is shown that macro and microforces consist of two parts, a nondissipative part, which can be derived from a free energy potential, and a dissipative part that can be considered as dissipative driving force. In contrast, the physical nature of microdefects can be difficult to identify for a specific brittle or ductile material. In addition, some computational issues are discussed in brief. To overcome these difficulties, various regularization techniques were proposed in the literature, using gradient enhancements of damage and hardening parameters and of strain measures.