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.

Although architected materials based on truss networks have been shown to possess advantageous or extreme mechanical properties, those can be highly affected by tolerances and uncertainties in the manufacturing process, which are usually neglected during the design phase. Deterministic computational tools typically design structures with the assumption of perfect, defect-free architectures, while experiments have confirmed the inevitable presence of imperfections and their possibly detrimental impact on the effective properties. Information about the nature and expected magnitude of geometric defects that emerge from the additive manufacturing processes would allow for new designs that aim to mitigate (or at least account for) the effects of defects and to reduce the uncertainty in the effective properties. To this end, we here investigate the effects of four most commonly found types of geometric imperfections in trusses, applied to eleven representative truss topologies in two and three dimensions. Through our study, we (i) quantify the impact of imperfections on the effective stiffness through computational homogenization, (ii) examine the sensitivity of the various truss topologies with respect to those imperfections, (iii) demonstrate the applicability of the model through experiments on 3D-printed trusses, and (iv) present a machine learning framework to predict the presence of defects in a given truss architecture based merely on its mechanical response.