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Biological structural designs in nature like hoof walls can be used as inspiration for generating structures with excellent mechanical properties. A common theme in these designs is the small percent porosity. Under dynamic transverse compression, we investigated the structure-property relations in low porosity structures. A diverse design space was created using polygonal tubules with different numbers of rows and columns. The volume fraction and the orientation angle of the tubules were also varied. The finite element method was used with a rate-dependent elastoplastic material model to generate the stress-strain curves in plane strain conditions. 

Previous studies show that the properties of parts manufactured via additive manufacturing, such as selective laser melting, depend on local feature sizes like lattice wall thickness and strut diameter. Although size dependence has been studied extensively, it was not included in constitutive models for numerical simulations. In this work, flat dog-bone tensile specimens of different thicknesses were manufactured and tested under quasi-static conditions to characterize the size-dependent properties experimentally. It was observed that key mechanical properties decrease with specimen thickness. Through curve-fitting to experimental data, this work provides approximate analytical expressions for the material properties values as a function of specimen thickness, furnishing a phenomenological size-dependent constitutive model. The interpolating capability of the model is cross-validated with existing experimental data. Two numerical examples demonstrate the application of the size-dependent material model. The axial crushing of thin-walled lattices at varying wall thicknesses was simulated by the size-dependent material model and one that ignores size effects. Results show that ignoring size effects leads to overestimated peak crushing force and specific energy absorption. The two material models were also compared in the topology optimization of thin-walled structures. Results show that the size-dependent model leads to a more robust optimized design: having higher energy absorption and sustaining less material fracture. 

This paper investigates the structure–property relations of thin-walled lattices, characterized by their cross-sections and heights, under dynamic longitudinal compression. These relations elucidate the inter- actions of different geometric features of a design on mechanical response, including energy absorption. We proposed a combinatorial, key-based design system to generate different lattice designs and used the finite element method to simulate their response with the Johnson–Cook material model. Using an autoencoder, we encoded the cross-sectional images of the lattices into latent design feature vectors, which were supplied to the neural network model to generate predictions. The trained models can accu- rately predict lattice energy absorption curves in the key-based design system and can be extended to new designs outside of the system via transfer learning.