发表机构
Eindhoven University of Technology（埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对机械超材料微形态计算均匀化中微观问题的高成本，提出结合本征正交分解与定制超降阶的降阶模型，数值实验验证了精度与在线加速，支持工程尺度大变形分析。
AI 中文摘要
机械超材料的一些奇异有效性质源于微观不稳定性，如屈曲和图案转变。其细观几何与局部和非局部效应的相互作用，使得直接数值模拟（DNS）成本过高，甚至难以处理。微形态计算均匀化（Rokos2019）已被提出以使宏观模拟可行：一个携带图案化波动场的代表性体积单元（RVE）解析微观尺度，而有效的微形态连续体描述宏观尺度。然而，此类模拟仍然昂贵，因为RVE问题及其相关的切线问题必须在每个宏观积分点求解，这在三维中尤其变得不可行。因此，我们提出了一种针对微观问题的降阶模型，将本征正交分解与针对微形态环境定制的超降阶方法相结合。两个数值示例量化了降阶基和超降阶误差，并讨论了离线成本和可实现的在线加速。结果表明，该方法能够实现机械超材料的工程尺度大变形分析。
英文摘要
Mechanical metamaterials owe some of their exotic effective properties to microstructural instabilities such as buckling and pattern transformation. Their fine-scale geometry, combined with the interplay of local and nonlocal effects, renders direct numerical simulation (DNS) prohibitively expensive, if not intractable. Micromorphic computational homogenization~\citep{Rokos2019} has been proposed to make macroscopic simulations feasible: a representative volume element (RVE) carrying patterning fluctuation fields resolves the microscale, while an effective micromorphic continuum describes the macroscale. Such simulations nevertheless remain costly, since the RVE problem and its associated tangent problems must be solved at every macroscopic integration point, which becomes prohibitive, especially in three dimensions. We therefore propose a reduced order model for the microscopic problem, combining proper orthogonal decomposition with a hyperreduction method tailored to the micromorphic setting. Two numerical examples quantify the reduced basis and hyperreduction errors and discuss the offline costs and attainable online speed-ups. The results show that this approach can enable engineering-scale large deformation analysis of mechanical metamaterials.
