  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.
