  In this study, a coarse-graining framework for discrete models is formulated
on the basis of multiscale homogenization. The discrete model considered in
this paper is the Lattice Discrete Particle Model (LDPM), which simulates
concrete at the level of coarse aggregate pieces. In LDPM, the size of the
aggregate particles follows the actual particle size distribution that is used
in experiment to produce concrete specimens. Consequently, modeling large
structural systems entirely with LDPM leads to a tremendous number of degrees
of freedom and is not feasible with the currently available computational
resources. To overcome this limitation, this paper proposes the formulation of
a coarse-grained model obtained by (1) increasing the actual size of the
particles in the fine-scale model by a specific coarsening factor and (2)
calibrating the parameters of the coarse grained model by best fitting the
macroscopic, average response of the coarse grained model to the corresponding
fine scale one for different loading conditions. A Representative Volume
Element (RVE) of LDPM is employed to obtain the macroscopic response of the
fine scale and coarse grained models through a homogenization procedure.
Accuracy and efficiency of the developed coarse graining method is verified by
comparing the response of fine scale and coarse grained simulations of several
reinforced concrete structural systems in terms of both accuracy of the results
and computational cost.
