The mechanical properties of nacre (mother-of-pearl), which are superior to those of its constituent materials, derive from a micro-architecture formed by the arrangement into parallel laminae of individual aragonite tiles with surface asperities, bonded by organic interlayers. A mechanical model is developed to determine how the contact profile that defines the geometry of the tile surface affects the constitutive response of hierarchical metamaterials of this type when they are strained in the lamellar plane. We consider the structured character of the deformation, consisting of elastic distortion of the tiles and the inelastic contribution from the disarrangements produced by relative sliding of the lamellar interfaces, which is formulated within the thermodynamic framework for irreversible processes in generalized materials. The resistance to sliding associated with constrained shear-induced dilatation of the tiles and the bridging of the organic interlayers are represented by a generalized cohesive-frictional law, effective at the level of averaged separation plane, providing a phenomenological approach that by-passes the difficulty in analytically solving the contact problem at asperities. The nominal stress–strain curves of the nacreous structure are shown to be highly dependent, qualitatively and quantitatively, on the geometry of the contact profiles. The model not only produces results that are in excellent agreement with experiments on nacre, but it can also describe complex stress–strain curves with pinched hysteresis loops having branches of various shapes, as well as serrated inelastic regimes. The versatility of this theoretical approach offers promise as a design tool for innovative metamaterials.

珍珠母（珍珠母）的机械性能优于其组成材料，源于一种微结构，该微结构由具有表面粗糙度的单个文石瓦片排列成平行薄片形成，由有机夹层粘合。开发了一个机械模型来确定定义瓷砖表面几何形状的接触轮廓如何影响这种类型的分层超材料在层状平面中应变时的本构响应。我们考虑变形的结构化特征，包括瓷砖的弹性变形和层状界面的相对滑动产生的无序的非弹性贡献，这是在广义材料中不可逆过程的热力学框架内制定的。与瓷砖的受约束的剪切引起的膨胀和有机夹层的桥接相关的滑动阻力由广义的内聚摩擦定律表示，在平均分离平面的水平上有效，提供了一种绕过困难的现象学方法在分析解决粗糙的接触问题。珍珠质结构的标称应力-应变曲线在质量和数量上都高度依赖于接触轮廓的几何形状。该模型不仅产生了与珍珠层实验非常一致的结果，而且还可以描述复杂的应力-应变曲线，其中包含具有各种形状分支的收缩磁滞回线，以及锯齿状的非弹性状态。