Complex mechanical behaviours are generally met in macroscopically homogeneous media as effects of inelastic responses or as results of unconventional material properties, which are postulated or due to structural systems at the meso/micro-scale. Examples are strain localization due to plasticity or damage and metamaterials exhibiting negative Poisson’s ratios resulting from special porous, eventually buckling, sub-structures. In this work, through ad hoc conceived mechanical paradigms, we show that several non-standard behaviours can be obtained simultaneously by accounting for kinematical discontinuities, without invoking inelastic laws or initial voids. By allowing mutual sliding among rigid tesserae connected by pre-stressed hyperelastic links, we find several unusual kinematics such as localized shear modes and tensile buckling-induced instabilities, leading to deck-of-cards deformations—uncapturable with classical continuum models—and unprecedented ‘bulky’ auxeticity emerging from a densely packed, geometrically symmetrical ensemble of discrete units that deform in a chiral way. Finally, after providing some analytical solutions and inequalities of mechanical interest, we pass to the limit of an infinite number of tesserae of infinitesimal size, thus transiting from discrete to continuum, without the need to introduce characteristic lengths. In the light of the theory of structured deformations, this result demonstrates that the proposed architectured material is nothing else than the first biaxial paradigm of structured continuum—a body that projects, at the macroscopic scale, geometrical changes and disarrangements occurring at the level of its sub-macroscopic elements.

复杂的力学行为通常在宏观上均一的介质中得到满足，这是非弹性响应的影响或非常规材料特性的结果，这是假定的或归因于介观/微观尺度的结构系统。例子是由于塑性或损坏引起的应变局部化，以及超材料由于特殊的多孔，最终屈曲的子结构而表现出负的泊松比。在这项工作中，通过临时设想机械范式，我们表明可以通过考虑运动学不连续性而同时获得几种非标准行为，而无需调用非弹性定律或初始空隙。通过允许通过预应力超弹性链节连接的刚性镶嵌体之间的相互滑动，我们发现了几种不寻常的运动学特性，例如局部剪切模式和拉伸屈曲引起的不稳定性，从而形成了卡片组变形（用经典的连续体模型无法捕获），以及以手性方式变形的离散单元的密密麻麻，几何对称的整体，出现了前所未有的“大”膨胀。最后，在提供了一些解析解和机械兴趣的不等式之后，我们达到了无限数量的无限小体的极限，从而从离散过渡到连续，而无需引入特征长度。根据结构变形理论，该结果表明，所提出的结构化材料无非是结构化连续体的第一个双轴范式-一个在宏观尺度上投影在其水平发生的几何变化和失序的物体亚宏观元素。