Lattice modeling of quasi-brittle materials, such as concrete, is a discrete mesoscale description of a material, where constitutive relations are defined at a lower scale compared to the continuum-based approaches. Over the years, these lattice discrete models have become increasingly efficient, and they are expected to be useful for generating high-fidelity databases of complex material responses. Such databases can be exploited in two ways: either to inform data-driven approaches or to calibrate macroscale models. In this paper, we focus on the latter. Macroscopic stress and strain responses are obtained by coarse-graining lattice discrete particle model (LDPM) responses. Stresses and strains are coarse-grained independently from computations on bending beams. Local and nonlocal scalar damage models are used to fit these data. The evolution of damage is constructed from these stress–strain responses by computing the pairs composed of damage and the history variable that govern its growth. Model parameters in the nonlocal model, including the internal length, are then obtained by fitting the macroscale constitutive model to the coarse-grained results. The global response of the bending beam (load vs. displacement) and the energy dissipation profiles provided by the calibrated nonlocal damage model are found to be consistent with LDPM results.
Khoury et al. (Mon,) studied this question.