Crystallization 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.

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.

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Several approaches are typically used to reduce torsional vibrations in mechanical systems with piston-driven engines [14,15]. Various types of f lexible couplings and dual-mass f lywheels are widely implemented [16][17]. It has been demonstrated that pneumatic tuners with adjustable torsional stiffness can be used to achieve active tuning of torsional vibrations [19][20][21][22][23]. Certain research ventures have focused on the application of nonlinear energy sink (NES) [24] and targeted energy transfer (TET) [25] with the goal of designing a device with quasi-zero torsional stiffness [26]. These research avenues require new approaches to solving analytical models. It is common practice in engineering that complicated systems are simplified -e.g. nonlinear systems are often linearised around an operating point. While in some cases linearisation is adequate as demonstrated in [27][28][29], there are applications that require nonlinear models because linearisation either does not provide sufficient accuracy, or is not possible at all [30].The first step in extending the linear model is the addition of a cubic term. Such a system, governed by the Duffing equation, has been the subject of numerous analyses [31]. Extensive mathematical tools have been developed to model the system, whether the nonlinearity is weak or strong.In this presented work, we decided to focus on a different type of a nonlinear system. Systems with power-law restoring force have not been extensively studied, in spite of the fact that they may occur naturally in many engineering problems. The source of nonlinearity can be contact law, such as Hertzian potential, for which restoring force f varies with displacement q as f ∝ q 1.5 . Further examples include systems without pre-tension or systems tuned to zero stiffness around the operating point. If the force-carrying medium is gas, such as in the pneumatic tuners [18], the restoring force is also inherently nonlinear with power-law dependence.

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.