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 thescaleatwhichcontinuum-basedconstitutiverelationsarewrittenusually. Themesostructureofthe materialisrepresentedexplicitly. Overtheyears,latticemodelshavebecomemoreandmoreefficient. Complex nonlinear responses at the macro-scale are obtained…
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 thescaleatwhichcontinuum-basedconstitutiverelationsarewrittenusually. Themesostructureofthe materialisrepresentedexplicitly. Overtheyears,latticemodelshavebecomemoreandmoreefficient. 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, continuum- based, 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.