本构集力学：在可容许本构定律集合上的变分力学
Constitutive-Set Mechanics: variational mechanics on an admissible set of constitutive laws
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中文总结 AI 辅助
本构集力学用可容许本构定律集合取代单一定律，通过占据测度上的支撑函数界定结构响应的最坏情况，并在多个力学问题中验证其鲁棒性。
中文摘要 AI 辅助
结构仿真需要本构定律，而实验很少能唯一确定一条本构定律：多条定律可能拟合相同的数据并满足相同的物理约束，但在结构以测试从未经历的方式加载时，这些定律之间会存在差异。本构集力学（CSM）保留所有这些定律。它在变分表述中用可容许集合取代单一定律，并让力学本身决定集合中的哪些成员影响结构预测。该框架基于一个观察：有限元装配仅在结构达到的应变处查询本构定律，因此增量能量通过这些应变的加权记录（即状态的占据测度）依赖于本构定律。集合下状态的能量是该测度上的支撑函数，而无论如何都会进行的平衡求解提供了界定最坏情况所需的信息。平衡状态成为鲁棒响应的证书，对任何力学求解器而言在保守侧严格，在全局最小化下则双侧严格；该证书的状态数最多比结构所查询的本构方向数多一个；一个相干性定理识别出逐点最坏材料何时不是任何单一材料所能达到的；本构推断也作用于同一支撑函数。该方法在线性弹性、数据约束的本构函数、相场断裂、组装的有限应变复合材料壳以及仅通过单模态测试表征的膜上得到演示。在壳上，结构查询了226个本构方向中的4个；在膜上，经认证的最坏情况能量超过参考值四倍以上，而最能缩小认证预测的实验并非本构不确定性最大的那个实验。
英文摘要
A structural simulation needs a constitutive law, and experiments rarely determine one uniquely: several laws may fit the same data and satisfy the same physical constraints, yet differ where the structure is loaded in ways the tests never were. Constitutive-Set Mechanics (CSM) keeps all of those laws. It replaces the single law in the variational formulation by the admissible set, and lets the mechanics itself decide which members of the set affect the structural prediction. The framework rests on one observation: a finite element assembly consults the law only at the strains the structure reaches, so the incremental energy depends on the law through a weighted record of those strains, the occupation measure of the state. The energy of a state under the set is a support function on that measure, and the equilibrium solve one performs anyway supplies the information needed to bound the worst case. Equilibrium states become certificates on the robust response, rigorous on the upper side for any mechanics solver and two-sided under global minimisation; the certificate has at most one more state than the number of constitutive directions the structure interrogates; a coherence theorem identifies when the pointwise-worst material is one no single material can be; and constitutive inference acts on the same support function. The method is demonstrated on linear elasticity, a data-constrained constitutive function, phase-field fracture, an assembled finite-strain composite shell, and a membrane characterised by one-mode tests alone. On the shell the structure interrogates four of 226 constitutive directions; on the membrane the certified worst-case energy exceeds the reference more than fourfold, and the experiment that most contracts the certified prediction is not the one where the constitutive uncertainty is largest.
发表机构
- Indian Institute of Technology Jammu（印度技术学院贾姆分校）
- Fudan University（复旦大学）
- Bauhaus-Universität Weimar（魏玛包豪斯大学）
- Leibniz University Hannover（汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。
