含球形孔洞材料弹性性质的梁模型
Beam model for the elastic properties of material with spherical voids
摘要：
本文用一种新的模型分析了具有等体积球形孔洞的材料的弹性性质，特别注意了孔洞的六方密排和面心立方排列。考虑远高于74%的空隙率，产生如开孔泡沫中的重叠空隙，因此产生连通的孔结构。材料由梁的网络表示。每个梁的弹性行为是从材料结构中解析得出的。通过计算梁网络的线弹性性质，计算了不同方向的杨氏模量和泊松比。在刚性损失的限制下，得到幂律，描述杨氏模量和空隙率之间的关系，弯曲主导方向的指数为5/2，拉伸主导方向的指数为3/2。相应的泊松比在0和1之间变化。随着空隙率的降低，这些指数分别变为2.3和1.3。分析和从新的梁模型获得的数据进行了比较，在同伴study中进行的有限元模拟，和良好的协议被发现。六角形紧密堆积的空隙排列功能非常各向异性的行为，相当于纤维增强材料，这可能会允许开孔材料的新应用。
英文摘要：
The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal close-packed and the face-centred cubic arrangement of voids. Void fractions well above 74 \% are considered, yielding overlapping voids as in an open-cell foam and hence a connected pore structure. The material is represented by a network of beams. The elastic behaviour of each beam is derived analytically from the material structure. By computing the linear elastic properties of the beam network, the Young's moduli and Poisson ratios for different directions are evaluated. In the limit of rigidity loss a power law is obtained, describing the relation between Young's modulus and void fraction with an exponent of 5/2 for bending-dominated and 3/2 for stretching-dominated directions. The corresponding Poisson ratios vary between 0 and 1. With decreasing void fraction, these exponents become 2.3 and 1.3, respectively. The data obtained analytically and from the new beam model are compared to Finite Element simulations carried out in a companion study, and good agreement is found. The hexagonal close-packed void arrangement features very anisotropic behaviour, comparable to that of fibre-reinforced materials, This might allow for new applications of open-cell materials.
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