Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials -- observed experimentally and in selected nonlinear simulations -- leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

翻译：旋节线超材料，其结构灵感来源于自然相分离过程，在设计具有极端性能的力学超材料时，为周期性和对称性形貌提供了重要替代方案。尽管其弹性力学性能已被系统确定，但其大变形非线性响应却难以预测和设计，部分原因是数据集有限且需要复杂的非线性模拟。本研究提出了一种新颖的物理增强机器学习与优化框架，专门用于解决在大变形场景下设计具有定制力学性能的复杂旋节线超材料所面临的挑战，这些场景中计算建模受限且实验数据稀疏。通过直接利用大变形实验数据，该方法促进了具有精确有限应变力学响应的旋节线结构的逆向设计。该框架揭示了旋节线超材料中由不稳定性诱导的图案形成现象——该现象已在实验和选定的非线性模拟中观察到——并通过非凸能量势形式的物理归纳偏置加以利用。总体而言，这种结合机器学习、实验与计算的工作为高效、准确地设计复杂旋节线超材料提供了一条途径，适用于能量吸收和非线性失效机制预测至关重要的大变形场景。