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Effective elastic properties of hexagonal and quadrilateral grid structures

机译:六角形和四边形网格结构的有效弹性

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The energetic homogenization procedure for the determination of the effective elasticity tensor of grid structures as proposed in an earlier paper is extended to the analysis of general hexagonal and quadrilateral grid structures. The method is based on the assumption that for macroscopically equal deformation the same strain energy has to be stored in a representative volume element whether the given microstructure or the effective homogenized medium is considered. The components of the effective elasticity tensor are determined by partial derivation of the strain energy density with respect to the macroscopic strain components. The analysis is performed comparatively by an analytical approach and by means of the finite element method. Standard commercial sandwich core geometries are considered as well as highly non-orthotropic grid structures. The influence of the cell geometry on the effective properties is discussed inn detail. Special interest is directed to negative Poisson's ratios as well as to effectively nonorthotropic elastic behavior.
机译:早先论文中提出的确定网格结构有效弹性张量的能量均匀化程序扩展到了对一般六角形和四边形网格结构的分析。该方法基于这样的假设:对于宏观上相等的变形,无论考虑给定的微观结构还是有效的均质介质,都必须将相同的应变能存储在代表性的体积元素中。有效弹性张量的分量通过相对于宏观应变分量的应变能量密度的部分推导来确定。该分析是通过分析方法和有限元方法进行的。考虑了标准的商用夹芯结构以及高度非正交各向异性的网格结构。详细讨论了单元几何形状对有效特性的影响。特别关注的是负泊松比以及有效的非正交各向异性弹性行为。

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