从梁模型确定二维胞状固体的Cosserat常数
Determining Cosserat constants of 2D cellular solids from beam models
摘要：
我们提出了一个两尺度模型的无序蜂窝材料的结果，我们描述的微观结构在一个理想化的方式使用梁网络模型，然后过渡到Cosserat型连续模型描述相同的材料在宏观尺度上。在这样的规模过渡，通常是自下而上的均匀化方法或自上而下的反向建模策略，以匹配宏观尺度Cosserat连续的微观尺度的梁网络。在这里，我们使用一种不同的方法，它是基于一个能量一致的连续化方案，使用从梁网络模型的数据，以确定连续的应力和应变变量在一组控制体积上定义的规模的个别微结构元素（细胞），以这样的方式，他们形成一个连续的镶嵌的材料域。应力和应变独立地确定在所有的控制体积，和本构参数获得的控制体积数据的合奏使用最小二乘误差标准。我们表明，这种方法产生的材料参数是经常蜂窝结构的分析结果密切一致。对于强烈无序的细胞结构，因此参数化Cosserat连续产生的结果，再现微观尺度梁模型的行为，无论是在所观察到的应变模式，并鉴于宏观响应，包括其大小的依赖性。
英文摘要：
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.
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