Energetic rigidity. I. A unifying theory of mechanical stability
Energetic rigidity. I. A unifying theory of mechanical stability
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DOI：
10.1103/physreve.105.025003
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发表时间：
2022-02-18
影响因子：
2.4
通讯作者：
Manning, M. Lisa
中科院分区：
文献类型：
--
作者：
Damavandi, Ojan Khatib;Hagh, Varda F.;Manning, M. Lisa
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，在这两篇论文中，我们提出了在实践中比两个更常用的刚性检验更有用的刚性概念：Maxwell-Calladine约束计数(一阶刚性)和二阶刚性。我们发现，只有当系统没有自应力状态时，约束计数才能很好地预测能量刚性。当系统处于自应力状态时，我们证明了在基于约束计数的不被认为是刚性的系统中，二阶刚度可以隐含能量刚性，并且甚至比剪切模数更可靠。我们还表明，可能存在一阶或二阶刚性都不意味着能量刚性的系统。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。
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 nontrivial 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.