Asymptotic Expansion Homogenization of Discrete Fine-Scale Models with Rotational Degrees of Freedom for the Simulation of Quasi-Brittle Materials

TL;DR

This paper develops a multiscale homogenization framework for discrete models with rotational degrees of freedom, enabling efficient simulation of quasi-brittle materials by deriving an equivalent Cosserat continuum.

Contribution

It introduces a general asymptotic analysis-based homogenization method applicable to any discrete model with rotations, producing a size-dependent micropolar continuum.

Findings

Homogenized elastic properties depend on RVE and heterogeneity sizes.

Size effects are significant in the elastic regime.

Coupling between stress-strain and couple-curvature is observed in nonlinear simulations.

Abstract

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.