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

摘要

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