论文标题
将局部能量学整合到麦克斯韦 - 卡拉丁的约束中，以设计机械超材料
Integrating local energetics into Maxwell-Calladine constraint counting to design mechanical metamaterials
论文作者
论文摘要
Maxwell-Calladine指数定理在我们当前对离散材料的机械刚性的理解中起着核心作用。通过考虑每个材料组件的几何约束，将每个材料组件强加于一组基本的自由度上，该定理将刚度的出现与约束计数参数联系起来。但是，麦克斯韦 - 卡拉丁范式受到了显着限制 - 其对约束和自由度之间的几何关系的独家依赖完全忽略了变形单个组件的实际能量成本。为了解决这一限制，我们基于自然融合了诸如刚度和预应力的局部能量特性的敏感性，得出了麦克斯韦 - 卡拉丁指数定理的概括。使用此扩展框架，我们研究了局部能量如何修改经典约束计数图片以捕获变形与外部力量之间的关系。然后，我们将这种形式主义与群体表示理论结合在一起，以设计机械超材料，其中利用了局部能量成本和结构性几何形状之间的对称性差异以控制对外力的反应。
The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees of freedom, the theorem relates the emergence of rigidity to constraint counting arguments. However, the Maxwell-Calladine paradigm is significantly limited -- its exclusive reliance on the geometric relationships between constraints and degrees of freedom completely neglects the actual energetic costs of deforming individual components. To address this limitation, we derive a generalization of the Maxwell-Calladine index theorem based on susceptibilities that naturally incorporate local energetic properties such as stiffness and prestress. Using this extended framework, we investigate how local energetics modify the classical constraint counting picture to capture the relationship between deformations and external forces. We then combine this formalism with group representation theory to design mechanical metamaterials where differences in symmetry between local energy costs and structural geometry are exploited to control responses to external forces.
