Lattice and continuum damage modeling for fracture of concrete

Lattice modelling of quasi-brittle materials such as concrete is a discrete, meso-scale, description of the material in which constitutive relations are prescribed at a lower scale compared to the scale at which continuum-based constitutive relations are written usually.The mesostructure of the material is represented explicitly.Over the years, lattice models have become more and more efficient.Complex nonlinear responses at the macro-scale are obtained today, while keeping the constitutive model at the meso-scale simple compared to macro-scale ones.Prediction capabilities and accuracy of the description of the mechanical response at the global level are, in many cases, better than those obtained with continuum-based models, although at the price of an intensive computational effort.In this work, we intend to draw a parallel between the Lattice Discrete Particle Model (LDPM) and a macro-scale damage model.For this, we implement first a coarse graining approach based on averaging the equations of conservation to convert lattice results into coarse-grained, continuumbased, stress versus strain responses.Because stresses and strains are coarse-grained independently, their relationship yields a database of macroscopic continuum responses.These data are then used to calibrate a non-local damage model.