非线性固体力学问题的分量级超降阶
Component-wise hyperreduction for nonlinear solid mechanics problems
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中文总结 AI 辅助
该研究提出分量级超降阶方法，通过POD与ECSW生成可复用的非线性固体力学分量，在大型准静态装配体中评估不足10%单元时误差低于1%，还可跨力学场景复用，为模块化模拟提供支持。
中文摘要 AI 辅助
超降阶的非线性固体力学分量可在离线阶段生成，并作为可转移构建块跨不同装配体、边界条件、网格、材料参数及本构模型复用。我们在分量层面使用本征正交分解（POD）与能量守恒采样加权（ECSW），并通过 mortar 网格绑定连接子结构。POD模态、ECSW权重及单元在离线阶段从单个分量的模拟中计算，每个子结构额外增加12个刚体模态以处理有限刚体运动。数值算例表明，在大型准静态装配体中，评估不足10%的单元时误差低于1%；尽管仅在弹性Neo-Hookean分量模拟上训练，相同分量基与ECSW单元已成功复用至有限应变黏弹性动力学场景。这些结果表明，分量级超降阶可为模块化非线性固体力学模拟提供可复用的降阶构建块。
英文摘要
Hyperreduced nonlinear solid-mechanics components can be generated offline and reused as transferable building blocks across different assemblies, boundary conditions, meshes, material parameters, and constitutive models. We use proper orthogonal decomposition (POD) and energy conserving sampling and weighting (ECSW) on the component level and connect the substructures by mortar mesh tying. The POD modes and the ECSW weights and elements are computed offline from simulations of single components and the finite rigid body motions are treated by 12 additional rigid body modes per substructure. The numerical examples demonstrate errors below 1 \% for large quasi-static assemblies while evaluating less than 10 \% of the elements. The same component bases and ECSW elements are successfully reused for finite-strain viscoelastic dynamics, although they were trained only on elastic Neo-Hookean component simulations. These results indicate that component-wise hyperreduction can provide reusable reduced building blocks for modular nonlinear solid-mechanics simulations.
