A Thermodynamic Framework for a Gradient Theory of Continuum Damage

Solanki, K.N., & Bammann, D. (2010). A Thermodynamic Framework for a Gradient Theory of Continuum Damage. Acta Mechanica. 213(1-2), 27–38.

In this paper, we present a formulation of state variable based gradient theory to model damage evolution and alleviate numerical instability associated within the post-bifurcation regime. This proposed theory is developed using basic microforce balance laws and appropriate state variables within a consistent thermodynamic framework. The proposed theory provides a strong coupling and consistent framework to prescribe energy storage and dissipation associated with internal damage. Moreover, the temporal evolution equation derived here naturally shows the effect of damage -nucleation, -growth and -coalescence. In addition, the theoretical framework presented here is easily extendable to the addition of other defects (not shown here), and can be generalized to the development of consistent coupled transport equations for species, such as hydrogen (Bammann et al. [1]), as well as providing a consistent structure for modeling events at diverse length scales.