AI 中文总结
本研究针对微结构可实现性约束，提出基于神经场与可微有限元的优化方法，设计接近理想变换弹性斗篷的宽带瑞利波地毯斗篷，其均质表示恢复约97%参考位移幅值，全解析微结构模拟恢复约76%。
AI 中文摘要
变换弹性为弹性动力学斗篷提供了合适的材料分布，但所需的刚度张量通常违反柯西弹性的 minor 对称性，难以用常规材料实现。现有方法通过修改变换后的张量来恢复这些对称性，仅能得到近似斗篷。本研究未修改变换后的张量，而是在柯西材料类别中寻找性能最佳的斗篷，将二维瑞利波地毯斗篷设计表述为偏微分方程约束的优化问题，采用基于坐标的神经场和可微有限元模型求解器，通过最小化波场畸变来优化对称刚度和密度场，考虑了单频和宽带优化，宽带模型在多个频率上训练。通过条件扩散、神经场逆设计和最近邻选择，利用均质微结构数据库解决物理可实现性问题。有限元模拟显示，优化后的柯西设计接近理想的基于变换的斗篷，投影到明确微结构后，均质表示恢复了约97%无缺陷参考表面位移幅值，而完全解析微结构几何的直接有限元模拟恢复了约76%。
英文摘要
Transformation elasticity provides appropriate material distributions for elastodynamic cloaks but the required stiffness tensors generally violate the minor symmetries of Cauchy elasticity and are difficult to realise using conventional materials. Existing approaches restore these symmetries by modifying the transformed tensor, producing only an approximate cloak. In this work rather than modifying the transformed tensor we seek the best performing cloak within the class of Cauchy materials. We formulate 2D Rayleigh wave carpet cloak design as an optimisation problem governed by partial differential equations. Using a coordinate based neural-field and a differentiable finite element model solver we optimise symmetric stiffness and density fields by minimising wave field distortion. Both single frequency and broadband optimisation are considered, with the broadband model trained over multiple frequencies. Physical realisability is addressed using a database of homogenised microstructures through conditional diffusion, neural-field inverse design, and nearest-neighbour selection. FEM simulations show that the optimised Cauchy design approaches the ideal transformation-based cloak. After projection onto explicit microstructures, the homogenised representation recovers approximately 97% of the defect free reference surface-displacement magnitude, while direct FEM simulation of the fully resolved microstructured geometry recovers approximately 76%
