Brittle response of concrete as a localization problem

A mathematical formulation for the mechanical response of concrete and similar cemented aggregate mixtures is presented. The stable response, associated with the growth of microcracks, is described by a phenomenological plasticity framework. The transition to unstable response, invoking localized deformation, is considered as a bifurcation problem. In the localized mode, the mechanical behaviour is modelled by estimating, through a homogenization technique, the average mechanical properties of a medium intercepted by a macrocrack. The strain-softening behaviour is the result of unstable response along the interface, triggered by a progressive degradation of surface asperities. The mathematical framework is illustrated by some numerical examples. The strain localization criterion, derived from considerations of stability of the constitutive relation governing the homogeneous deformation mode, is applied to determine the bifurcation point and the orientation of the macrocrack in a series of plane strain tests. The simulations of unstable response are also provided, illustrating the effect of the size of the sample on average mechanical characteristics. The formulation is incorporated in a finite element code to investigate the progressive failure of concrete blocks subjected to uniaxial compression.