Stress-strain constitutive relations and Poisson’s ratios are fundamental properties of naturally occurring materials, based on which their mechanical applications can be designed. The lack of tailorability and restricted margin for such critical properties severely limit the bounds of achievable multi-functional engineering designs using conventional materials. Through analytical and numerical analyses, supported by elementary-level physical experiments, we have proposed a kirigami-inspired hybrid metamaterial with programmable deformation-dependent stiffness and mixed-mode multidirectional auxeticity. The metamaterial can transition from a phase of low stiffness to a contact induced phase that brings forth an extensive rise in stiffness. Uniform and graded configurations of multi-layer tessellated material are developed to modulate the constitutive law of the metastructure with augmented programmability in two- and three-dimensional spaces. The proposed metamaterial will lead to extreme lightweight functional designs for impact resistance, shape morphing, multidirectional deformation, vibration and wave propagation control, where the capabilities of intrinsic material can be most optimally exploited.

应力-应变本构关系和泊松比是天然存在的材料的基本属性，可以根据这些属性设计其机械应用。这种关键特性缺乏可裁剪性和有限的裕度，严重限制了使用传统材料可实现的多功能工程设计的范围。通过分析和数值分析，在初级物理实验的支持下，我们提出了一种受剪纸启发的混合超材料，具有可编程的变形相关刚度和混合模式多向拉伸性。超材料可以从低刚度阶段过渡到接触诱导阶段，从而大大提高刚度。开发了多层镶嵌材料的均匀和分级配置，以在二维和三维空间中通过增强的可编程性来调节超结构的本构规律。拟议的超材料将导致用于抗冲击、形状变形、多向变形、振动和波传播控制的极轻功能设计，其中可以最优化地利用固有材料的能力。