Architected solids, typically manufactured by additive manufacturing, contain a limited number of unit cells and therefore resemble discrete structures rather than continuum materials. The number of unit cells in a specimen of an architected solid is referred to here as the specimen size. Using extensive finite element simulations complemented by analytical analysis, we demonstrate counterintuitive specimen-size effects across several classes of architected solids subjected to different loading conditions. In contrast to conventional continuum materials, size effects are strongest under uniaxial loading, where the applied loading does not impose a macroscopic stress/ strain gradient, and are comparatively weak under indentation loading, which imposes strong stress/strain gradients. Moreover, smaller could be either stiffer or more compliant dependening on the lattice topology and/ or nature of loading. Two key mechanisms governing these size effects are identified: free-surface effects arising from differences in strut sharing between surface and bulk unit cells, and size-dependent changes in deformation mode from bending-dominated to stretching-dominated behavior. Consequently, no universal size-effect trend exists; instead, stiffness depends on both lattice topology and loading mode. These findings highlight the need for caution when extracting effective material properties from experiments on architected solids with a limited number of unit cells.

Capturing high-rate spatiotemporal deformation of materials in three dimensions (3D) remains a significant challenge with current X-ray imaging techniques. We present a methodology that combines advances in neural rendering techniques with volume correlation methods to accurately reconstruct complex, high-rate 3D spatiotemporal structural evolutions. The fidelity and versatility of the method, which requires no pretraining, are demonstrated for a diverse set of intricate 3D-printed microarchitected solids. Using laboratory-based X-ray tomography, we capture the 3D growth of a high-rate crush band on a timescale of less than 100 ms. By broadening this idea to a stereo X-ray concept, we eliminate the need to rotate the image object, thereby extending the technique to significantly faster timescales. Our neural rendering framework opens possibilities for 3D observations of viscoelastic responses of biological materials to 3D investigations of numerous poorly understood dynamic processes, such as the runaway failure of batteries, all using laboratory X-ray systems.

Interrupted X-ray computed tomography (X-CT) has been the common way to observe the deformation of materials during an experiment. While this approach is effective for quasi-static experiments, it has never been possible to reconstruct a full 3d tomography during a dynamic experiment which cannot be interrupted. In this work, we propose that neural rendering tools can be used to drive the paradigm shift to enable 3d reconstruction during dynamic events. First, we derive theoretical results to support the selection of projections angles. Via a combination of synthetic and experimental data, we demonstrate that neural radiance fields can reconstruct data modalities of interest more efficiently than conventional reconstruction methods. Finally, we develop a spatio-temporal model with spline-based deformation field and demonstrate that such model can reconstruct the spatio-temporal deformation of lattice samples in real-world experiments.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work we present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.

Crystallization of dry particle assemblies via imposed vibrations is a scalable route to assemble micro/macro crystals. It is well understood that there exists an optimal frequency to maximize crystallization with broad acceptance that this optimal frequency emerges because high-frequency vibration results in overexcitation of the assembly. Using measurements that include interrupted X-ray computed tomography and high-speed photography combined with discrete-element simulations we show that, rather counterintuitively, high-frequency vibration underexcites the assembly. The large accelerations imposed by high-frequency vibrations create a fluidized boundary layer that prevents momentum transfer into the bulk of the granular assembly. This results in particle underexcitation which inhibits the rearrangements required for crystallization. This clear understanding of the mechanisms has allowed the development of a simple concept to inhibit fluidization which thereby allows crystallization under high-frequency vibrations.

AbstractCrystallization of granular assemblies has broad implications for rapid and scalable creation of architected materials with applications ranging from structural materials to microarchitected battery electrodes. While significant advances have been made in understanding colloidal self‐assembly at nano to micro scale, the governing mechanisms for organization of dry assemblies of hard spheres remain unclear. Here, we investigate crystallization of mono‐size hard spheres with and without imposed vibration. Using X‐ray computed tomographic analysis coupled with discrete‐element simulations, we unravel the roles of gravity and imposed vibration on the three‐dimensional self‐assembly of the dry spheres. We use these insights to introduce gravity‐mediated epitaxial crystal growth with slow pouring of balls on seeding templates. Contrary to vibration‐induced crystallization, this method can form large single crystals with both close‐packed and rather surprisingly, nonclose‐packed metastable particle arrangements. Our results provide insight for the scalable manufacture of defect‐free granular assemblies that can be used as space‐holding templates to manufacture cellular materials, such as inverse opals and other related topologies.Key points Self‐assembly of hard spheres is a critical step for the scalable manufacture of micro‐architected solids. Via a combination of vibration experiments, 3D X‐ray tomographic observations, and simulations, we elucidate the critical role of gravity in the self‐assembly of hard spheres. We design seeding templates that can not only induce the self‐assembly into stable close‐packed crystal structures but also rather counterintuitively into metastable single crystal structures.

Modern-day approaches to reducing the emissions of combustion engines lead to unconventional strategies which include downspeeding, downsizing, cylinder deactivation. A common characteristic of these strategies is a shift in torque excitation components of the combustion engine. This excitation shift results in an increase in vibrations of the drivetrain and the risks associated with it. The presented article aims to investigate the elementary characteristics of the pure cubic nonlinear system and to identify the potential for its use in mechanical systems.

To model the nonlinear behaviour of vibrating systems, Taylor expansion with integer powers is often used. Some systems, however, are inherently nonlinear. In the case of a non-integer real exponent, the power-law system cannot be linearised around the equilibrium position using Taylor expansion. The approach presented here provides a simple estimate of the principal frequency of free vibration in systems with power-law restoring force. Without seeking the precise mathematical form of the output waveform, we only focus on the principal frequency. The first step is the use of dimensional analysis to reduce the number of parameters. Two independent non-dimensional groups are formed and functional dependence between them is sought using numerical simulations. Once this dependence is known, the principal frequency of free vibration can be readily determined for any system properties and any initial conditions. Finally, we compare the numerical results to analytical expressions for a few restoring force exponents.