Modeling of micromorphic continuum based on a heterogeneous microscale

Abstract

Generalized continuum theories have emerged as a promising solution for the limitations of traditional continuum mechanics in fully describing the behavior of materials in which the influence of the microstructure is not negligible. The macroscopic response of quasi-brittle material, for example, is closely tied to its heterogeneous microstructure and the simplifying hypothesis of classical theory is insufficient to address all the phenomena involved. By incorporating a length scale associated to the microscale, generalized continua can handle localization issues in quasi-brittle materials represented as elastic-degrading media. An important drawback that greatly limits the applicability of such generalized models is the definition of the numerous elastic parameters. Taking into account the micromorphic theory, 18 constants are required for the description of an isotropic medium. In this paper, a numerical approach for determining the micromorphic constitutive relations, previously applied only for a homogeneous medium, is detailed based on the homogenization of a heterogeneous microscale. The microstructure 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. 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. Afterwards, a simulation is presented wherein the localization phenomenon is detected and a damage model specifically proposed for the micromorphic continuum is employed. This work could lead to models that are able to capture the microstructure influence, often disregarded when modeling quasi-brittle media, within the framework of generalized continuum theory, while also addressing the challenge of defining the elastic parameters.