For the load paths with small or no confining pressure, the nucleation, growth, and coalescence of cracks and micro-cracks are the main sources of non-linearity in the observed behavior of concrete. The formations of cracks and micro-cracks destroy material bonds and render the material more compliant. These are typically irreversible internal changes and lead to strong directionality in concrete response. To model such nonlinear material behavior, a constitutive law for concrete utilizing damage mechanics is presented for small and isothermal deformations. The general theory is cast within the framework of the internal variable theory of thermodynamics where the dissipation inequality is used. A damage criterion is subsequently obtained using a damage function and the loading-unloading statement is provided. The decomposition of the compliance tensor into damaged and undamaged states is outlined and the flow rules for the inelastic strains are provided. Specific damage response tensors for isotropic and anisotropic modeling is proposed along with numerical simulations that are plotted for illustrating differences between isotropic and anisotropic formulations.
Full Text (PDF)