Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb.

使用细长梁理论推导出六边形蜂窝的小应变、平面内、弹塑性响应的精确解；蜂窝的不可压缩性是通过用不可压缩的无粘性流体填充其空隙来增强的。蜂窝具有等长的边，但其倾斜的支柱所对的角度可能与垂直侧壁成 120° 的偏差。相对密度足够小，支柱很细长，可以作为欧拉-伯努利梁处理。在一般面内载荷下，获得了刚性理想塑性晶格的弹性模量和宏观屈服面的精确解：这些解满足每个弹性理想塑性梁的平衡、相容性和本构响应。在进行弹性分析和刚性理想塑性分析之前，可压缩的六角桁架的版本。从运动学矩阵的零空间确定了可压缩蜂窝的两种非拉伸坍塌机制。蜂窝状空隙中不可压缩的无粘性流体的存在会锁定一种机制，但另一种机制仍然存在并产生宏观剪切应变。因此，具有刚性接头的不可压缩六边形蜂窝具有高剪切柔量和低剪切强度，其值与未填充的可压缩蜂窝相同。相比之下，不可压缩蜂窝体的宏观拉伸应变除了棒材弯曲外还需要拉伸棒材，从而提高不可压缩蜂窝体的拉伸模量和强度。