A continuum model of micro-cracks in concrete

The aim of this study is to propose a model describing the evolution of the mechanical properties of micro-cracked bodies under slow mechanical loading. To do so, we consider each material element of the body as a domain of finite size comprising one single crack. The size and orientation of the latter are treated as Lagrangian coordinates that are complementary to those usually describing the translations of the material elements. As such, their evolution is driven by some balance equations that are provided by the theory of continua with microstructure and by fit constitutive equations. To deal with the latter, we then call upon fracture mechanics. The model is applied to concrete within some simplifying assumptions and the case of a bar tensioned by a hard device is studied. Crack propagation and stiffness loss are determined when the loading increases, they are compared to experimental results.