Micromorphic two-scale modelling of periodic grid structures
Micromorphic two-scale modelling of periodic grid structures
复制标题
周期性网格结构的微形态二尺度建模
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Diebels
中科院分区：
文献类型：
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作者：
R. Jänicke;H. Sehlhorst;A. Düster;S. Diebels
目前的贡献集中在周期性网格结构的数值均匀化方面。为了研究微观到宏观尺度的转变，我们将提出一个一致的数值均匀化方案，在宏观尺度上用均匀的微观形态替代非均匀的柯西微观连续体。扩展的自由度，即微变形及其梯度，应根据几何变形模式和相关的单元单元的加载条件来解释。假定宏观尺度和微观尺度的应变能等价，识别了正方形和蜂窝网格结构的有效本构性质，并与微观分辨率的参考计算进行了比较，定量地验证了其有效本构性质。
The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution.