  Discrete fine-scale models, in the form of either particle or lattice models,
have been formulated successfully to simulate the behavior of quasi-brittle
materials whose mechanical behavior is inherently connected to fracture
processes occurring in the internal heterogeneous structure. These models tend
to be intensive from the computational point of view as they adopt an a priori
discretization anchored to the major material heterogeneities (e.g. grains in
particulate materials and aggregate pieces in cementitious composites) and this
hampers their use in the numerical simulations of large systems. In this work,
this problem is addressed by formulating a general multiple scale computational
framework based on classical asymptotic analysis and that (1) is applicable to
any discrete model with rotational degrees of freedom; and (2) gives rise to an
equivalent Cosserat continuum. The developed theory is applied to the upscaling
of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete
model for concrete and other quasi-brittle materials, and the properties of the
homogenized model are analyzed thoroughly in both the elastic and inelastic
regime. The analysis shows that the homogenized micropolar elastic properties
are size-dependent, and they are functions of the RVE size and the size of the
material heterogeneity. Furthermore, the analysis of the homogenized inelastic
behavior highlights issues associated with the homogenization of fine-scale
models featuring strain-softening and the related damage localization. Finally,
nonlinear simulations of the RVE behavior subject to curvature components
causing bending and torsional effects demonstrates, contrarily to typical
Cosserat formulations, a significant coupling between the homogenized
stress-strain and couple-curvature constitutive equations.
