Study of the Inclusion of Heterogeneity in the Determination of Constitu- tive Relations for Micromorphic Media through Homogenization

Resumo

The behavior of quasi-brittle materials, such as concrete, is closely tied to their heterogeneous structure, leading to complex responses to applied loads, including the formation of localized zones of damage. Traditional continuum mechanics models fail to adequately consider the influence of microstructure. To address this limitation, generalized continuum theories have emerged, such as the micromorphic theory, which incorporates additional degrees of freedom to capture the material’s microstructure. Additionally, these theories can effectively handle localization issues in quasi-brittle materials represented as elastic-degrading media due to their nonlocal nature. In this study, we investigate the influence of heterogeneity on determining constitutive relations for micro-
morphic media using a homogenization approach, with a particular focus on quasi-brittle materials. By employing a homogenization technique, the effective constitutive relations for the micromorphic continuum are obtained considering the heterogeneity in a finer-scale. This miscrostructure formed by aggregates and matrix considered in the finer-scale is generated by the take-and-place algorithm and its behavior is described by a classical continuum. Furthermore, an important challenge when modeling with the micromorphic theory is the determination of the 18 elastic parameters required for an elastic isotropic medium. To overcome this obstacle, through this homogenization framework, only classical parameters for the microstructure components are required for the analysis. An analysis is here conducted in order to understand the effect of different characteristics of the finer-scale, as mesh, microcontinuum size, and heterogeneity distribution, on the resulting macroscopic micromorphic constitutive relations. This work could lead to models that are able to capture the microstructure influence, often disregarded when modeling quasi-brittle media, associated to a generalized continuum theory.