能量刚性I：机械稳定性的统一理论
Energetic rigidity I: A unifying theory of mechanical stability
摘要：
刚性调节许多物理和生物系统的完整性和功能。这是关于刚性起源的两篇论文中的第一篇，其中我们提出“能量刚性”，其中所有非平凡的变形都会提高结构的能量，这是一个比两个更常用的刚性测试更有用的刚性概念：Maxwell-Calladine约束计数（一阶刚性）和二阶刚性。我们发现，约束计数鲁棒地预测能量刚性只有当系统没有自应力状态。当系统具有自应力状态时，我们证明了二阶刚度可以在基于约束计数不被认为是刚性的系统中暗示能量刚度，并且比剪切模量更可靠。我们还表明，可能有系统的第一或第二阶刚度意味着精力充沛的刚性。能量刚性的形式主义统一了我们对机械稳定性的理解，也为材料设计提供了新的途径。
英文摘要：
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self stress. When the system has states of self stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.
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