Rational Damage Model of 2D Disordered Brittle Lattices Under Uniaxial Loadings

The article presents a statistical rational model of damage for 2D disordered spring networks under a generic uniaxial loading. The validation is carried out by using the output from numerical simulations of compression and tension tests along the coordinate axes x and y. The findings demonstrate that the rational model works flawlessly in the hardening and softening phases, both for compression and for tension. A clear and intuitive definition of the damage parameter D (stated in two alternative forms) is obtained in terms of the combination of three random fields {ε ^* _p , η _p , n _p }, which fully encapsulate the complexity of the damage and act as input parameters of the rational model. The analysis of these parameters shed new light on the homogeneous—heterogeneous phase transition of disordered brittle materials and opens up new possibilities in studying and modeling damage processes. The limits of the scalar formulation are also outlined. Simplified models of the rational model are derived and discussed to prove that the apparent complexity of {ε ^* _p , η _p , n _p } can be administered by identifying ad hoc simplifying assumptions. The theory is developed for a 2D network but the underlying ideas are general.