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：旋节线超材料以其受自然相分离过程启发的构型，在设计具有极端性能的力学超材料时，已成为周期性和对称形态的重要替代方案。尽管其弹性力学特性已被系统测定，但大变形非线性响应的预测与设计仍具挑战，部分原因是数据集有限且需要复杂的非线性模拟。本文提出了一种新颖的物理增强机器学习与优化框架，专门应对在计算模型受限且实验数据稀疏的大变形场景下，设计具有定制力学性能的复杂旋节线超材料的难题。通过直接利用大变形实验数据，该方法实现了对旋节线结构的逆向设计，使其具备精确的有限应变力学响应。该框架揭示了旋节线超材料中失稳诱导的图案形成机制——该现象在实验及特定非线性模拟中均被观察到——并通过非凸能量势的形式引入基于物理的归纳偏置。综上所述，这种融合机器学习、实验与计算的方法，为在能量吸收及非线性失效机制预测至关重要的大变形场景中，高效且精确地设计复杂旋节线超材料提供了一条可行路径。