周期弹性晶格均匀化引发的材料失稳及后续再稳定
Material instability and subsequent restabilization from homogenization of periodic elastic lattices
AI总结：
本研究通过二维均匀化推导两类周期弹性晶格等效的非线性弹性材料，发现压缩载荷下材料失稳后可因单元轴向柔度实现再稳定，为制备可调失稳特性的点阵材料与可重构材料提供新方向。
摘要：
通过二维均匀化方法推导得到两类非线性弹性材料。这类材料等效于由可轴向变形且带轴向预载的结构单元组成的周期网格，承受包含弯曲、剪切和法向力的增量变形。其中一类材料的单胞特征为变形集中在有限自由度框架内的单元；另一类则为弥散变形，采用轴向柔度足够大的可弯曲杆模型。随着压缩载荷增大，等效材料的弹性张量失去正定性，随后发生椭圆性丧失。值得注意的是，在特定条件下，这种失稳之后会出现后续再稳定：即材料重新进入椭圆区域甚至正定性域，同时底层弹性晶格恢复稳定状态。该效应与单元的轴向柔度密切相关。我们的结果：（1）展示了利用弹性范围内、具有有限自由度的结构单元制备具备可调失稳特性的点阵材料的新可能；（2）提出了以稳定或失稳“岛”为特征的可重构材料。
英文摘要：
Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental deformations that involve bending, shear, and normal forces. The unit cell of one class is characterized by elements where deformations are lumped within a finite-degrees-of-freedom framework. In contrast, the other class involves smeared deformation, modelled as flexurally deformable rods with sufficiently high axial compliance. Under increasing compressive load, the elasticity tensor of the equivalent material loses positive definiteness and subsequently undergoes an ellipticity loss. Remarkably, in certain conditions, this loss of stability is followed by a subsequent restabilization; that is, the material re-enters the elliptic regime and even the positive definiteness domain and simultaneously, the underlying elastic lattice returns to a stable state. This effect is closely related to the axial compliance of the elements. Our results: (i.) demonstrate new possibilities for exploiting structural elements within the elastic range, characterized by a finite number of degrees of freedom, to create architected materials with tuneable instabilities, (ii.) introduce reconfigurable materials characterized by 'islands' of stability or instability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
