Determining Cosserat constants of 2D cellular solids from beam models

TL;DR

This paper introduces a novel energetically consistent method to determine Cosserat continuum parameters from beam network models of 2D cellular solids, effectively bridging microstructure and macro-scale behavior.

Contribution

It presents a new approach for scale transition that accurately derives Cosserat constants from microstructural data using a least-squares fit, improving modeling of disordered cellular materials.

Findings

Accurately predicts Cosserat parameters for honeycomb structures.

Reproduces micro-scale behavior in disordered cellular structures.

Captures size-dependent macroscopic responses.

Abstract

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.