The mechanical behavior of bulk materials is defined by their stress-strain curves, reflecting intrinsic microstructural properties. Additive manufacturing (AM) allows for tailoring mechanical properties through the micro-architecture of 3D metamaterials, enabling unusual properties like negative Poisson's ratio, negative compressibility, and shape recoverability. While forward design, topology optimization, and machine learning approaches have been used, they haven't accurately captured all desired mechanical behaviors due to non-unique response-to-design mappings and manufacturing challenges. Process variabilities and defects lead to significant deviations from designed properties, potentially causing suboptimal or catastrophic failure. This research presents a novel rapid inverse design methodology to address these limitations.

Existing methods for designing architected metamaterials with specific mechanical properties include forward design approaches, topology optimization, and machine learning techniques. Forward design iteratively adjusts parameters until desired properties are achieved, requiring significant expertise. Topology optimization and ML-based methods show promise but struggle to accurately capture the full range of mechanical behaviors, especially considering the non-unique mapping between design and response, and the influence of manufacturing defects and process variabilities. The current methods often result in substantial discrepancies between the designed and actual properties of fabricated samples.

This study introduces a rapid inverse design methodology that leverages generative machine learning and desktop 3D printing. The methodology employs a generative ML pipeline with inverse prediction and forward validation modules, each comprised of five neural networks (NNs). The input to the inverse prediction module is a user-defined uniaxial compressive stress-strain curve (represented by curve features) and fabrication parameters (maximum build volume and minimum printable feature size). The output is a set of optimal design parameters describing a digital lattice design. A family of architectural unit cells was developed to capture diverse curve shapes under monotonic and cyclic loadings, serving as building blocks for training data. The training data incorporates two different polymeric materials (brittle and flexible) to account for material properties and manufacturing errors. The generative ML pipeline learns the relationship between mechanical behaviors, topology, and manufacturing errors. The forward validation module predicts the stress-strain curve for a given design, allowing for comparison with the target curve and selection of the optimal design. This embedded approach addresses the non-unique response-to-design mapping issue. The design space is formulated as a dimensionless space encompassing various stress-strain curve shapes, incorporating theoretical bounds of elastic stiffness and yield strength. The input stress-strain curve is parameterized into 46 curve features, used as input for the ML pipeline. The training dataset includes hundreds of basic architectural configurations, each tessellated to create 3D lattice models. Samples were 3D printed, and their stress-strain curves were measured and parameterized to create the X-Y pairs for training. Data augmentation was used to account for prediction fluctuations. The forward module is trained first, then frozen while training the inverse module to prevent instability. The accuracy of the ML approach was evaluated using 10-fold cross-validation. Finite element simulations were used for creating the training datasets for compound lattices. A sequential integration strategy was adopted for the inverse design of compound lattices, where design parameters are varied within the lattice volume. The mechanical properties were tested using an Instron universal testing machine for both monotonic and cyclic compression. Drop tests were used for evaluating the energy absorption performance of compound lattices.

The generative ML pipeline successfully created metamaterials replicating a wide range of uniaxial compressive stress-strain curves, including linear-elastic behavior, strain softening/hardening, tunable tangent modulus, yielding, fracture, and multiple stress peaks and valleys. The approach accurately accounted for 3D printing defects and uncertainties, achieving approximately 90% fidelity between target and experimental results for both monotonic and cyclic loading. The normalized root-mean-square error (NRMSE) between target and measured curves was close to zero for all cases. The methodology was robust to variations in the 3D printing process variability. The inverse design of an architected shoe midsole demonstrated the ability to tailor the material's dynamic performance by adjusting stress-strain curves in different sections of the midsole to optimize running performance. The use of compound lattices, with spatially varying design parameters, enabled the creation of advanced stress-strain curves with features not found in natural materials, such as variable tangent modulus and multiple peaks and valleys. Manipulating pairs of design gradients allowed fine control of these advanced curve features, providing precise control over the stress-strain response. Experimental validation of the inversely designed compound lattices confirmed the ability to create materials with tailored softening effects and multiple stress peaks. Drop tests showed significant improvement in energy absorption performance compared to previously reported lattice materials.

This study's findings demonstrate a significant advancement in the rapid inverse design of metamaterials. The high accuracy in replicating desired mechanical behaviors, even while accounting for manufacturing imperfections, addresses a major limitation of previous approaches. The ability to design materials with advanced stress-strain curve features opens up new possibilities for creating materials with tailored energy absorption and other specialized functions. The speed and efficiency of the ML-based approach significantly reduce the time and cost associated with traditional design-manufacturing cycles. The success in creating a functional, tailored shoe midsole showcases the practical applicability of this methodology.

This work presents a rapid and accurate ML-based inverse design methodology for creating metamaterials with precisely tailored mechanical behavior. The approach successfully accounts for process-dependent errors, achieving high fidelity between target and experimentally measured results. The demonstrated ability to design complex stress-strain curves, including advanced features, expands the possibilities for creating high-performance materials with specific applications. Future work could focus on expanding the methodology to other material systems, loading conditions, and material properties, and exploring the use of transfer learning to accelerate the design process for different additive manufacturing techniques.

The current study focused primarily on uniaxial compressive behavior and utilized two specific polymeric materials. While the methodology showed robustness to process variability within the tested range, further investigation is needed to evaluate its performance across a broader range of manufacturing processes and materials, particularly metal additive manufacturing, where anisotropy and other material processing effects may be more significant. The impact of other manufacturing defects not considered in the training data, such as porosity and shrinkage, should also be studied in future research. The application to dynamic loading was investigated through scaling relations with quasistatic data, which could be further improved by incorporating dynamic loading in training datasets.