发表机构
University of California, Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种零体积模量的铰接蜂窝结构，通过特殊界面设计保留超过五分之四的剪切模量，性能优于Milton构造，可用于需适配尺寸变化的工程场景。
AI 中文摘要
泊松比接近-1仅表明体积模量与剪切模量相比较小。在固体-空隙结构中，使膨胀自由的机制通常也会削弱抗剪切能力，导致两个模量都变小。在二维线性弹性中，我们证明这种损失并非不可避免。我们考虑由单一不可压缩各向同性弹性固体的正六边形块组成的蜂窝结构，这些块沿整个边缘通过理想界面连接，该界面允许沿与边缘法线倾斜的方向相对滑动。集体无穷小的块旋转产生精确的膨胀机制，因此有效体积模量消失，而六重对称性确保各向同性。然而，这些界面沿其整个长度传递牵引力。在固体-空隙实现中，每个界面被替换为由空隙分隔的细固体板，这些板易弯曲但仍保留传递轴向力的能力。这种膨胀材料可自由膨胀或收缩，同时抵抗任何形状变化，可作为中间层，在适应热或膨胀失配的同时仍传递剪切力，还可作为支架和可展开结构的部件，这些结构改变尺寸但不改变形状。显式的、静力学可容许的应力场和互补能量原理给出了保留剪切模量的严格下界，极限论证将该下界转移到固体-空隙混合物。该蜂窝结构在体积模量为零时保留了其组成材料超过五分之四的剪切模量：此类混合物的归一化剪切模量的上确界S满足S > 0.8528 > 4/5，超过Milton构造所达到的值。
英文摘要
A Poisson's ratio near -1 indicates only that the bulk modulus is small compared with the shear modulus. In solid-void structures, the mechanism that frees the dilation usually weakens the resistance to shear as well, resulting in both moduli becoming small. In two-dimensional linear elasticity, we demonstrate that this loss is not inevitable. We consider a honeycomb of regular hexagonal blocks of a single incompressible isotropic elastic solid, joined along their whole edges by ideal interfaces that allow relative sliding along a direction inclined to the edge normal. Collective infinitesimal block rotations produce an exact dilational mechanism, so the effective bulk modulus vanishes, while sixfold symmetry ensures isotropy. The interfaces, however, transmit traction along their whole length. In a solid-void realization, each interface is replaced with fine solid plates separated by void, which bend easily yet retain their capacity to transmit axial force. Such dilational materials, which expand or contract freely while resisting every change of shape, could serve as interlayers that accommodate thermal or swelling mismatch while still transmitting shear, and as components in stents and deployable structures that change size without changing shape. An explicit, statically admissible stress field and the complementary energy principle yield a rigorous lower bound on the retained shear modulus, and a limiting argument transfers this bound to the solid-void mixtures. The honeycomb retains more than four-fifths of its constituent's shear modulus at zero bulk modulus: the supremum S of the normalized shear modulus of such mixtures satisfies S > 0.8528 > 4/5, exceeding the value attained by Milton's construction.
Comments17 pages, 3 figures
