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 modeling 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.

中文翻译：

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从光束模型确定二维细胞固体的Cosserat常数

我们提出了无序细胞材料的两尺度模型的结果，其中我们使用束网络模型以理想的方式描述了微观结构，然后过渡到了描述宏观尺度上相同材料的Cosserat型连续体模型。在这样的尺度转换中，通常使用自下而上的均质化方法或自上而下的反向建模策略，以使宏观尺度的Cosserat连续体与微观尺度的射束网络相匹配。在这里，我们使用一种不同的方法，该方法基于能量一致的连续方案，该方案使用梁网络模型中的数据来确定一组控制体积中的连续应力和应变变量，这些控制体积是根据单个微结构元素（单元）的规模定义的以它们形成材料域的连续细分的方式。在所有控制体积中独立确定应力和应变，并使用最小二乘误差准则从控制体积数据集合中获得本构参数。我们表明，这种方法产生的材料参数与解析结果非常吻合，适用于常规蜂窝结构。对于高度混乱的细胞结构，