Design of Pseudo-Mechanisms and Multistable Units for Mechanical Metamaterials

Transformable Superisostatic Crystals Self-Assembled from Segment Colloidal Rods

Transformable mechanical structures can switch between distinct mechanical states. Whether this kind of structure can be self-assembled from simple building blocks at microscale is a question to be answered. In this work, we propose a self-assembly strategy for these structures based on a nematic monolayer of segmented colloidal rods with lateral cutting. By using Monte Carlo simulation, we find that rods with different cutting degrees can self-assemble into different crystals characterized by bond coordination z that varies from 3 to 6. Among these, we identify a transformable superisostatic structure with pgg symmetry and redundant bonds (z = 5). We show that this structure can support either soft bulk modes or soft edge modes depending on its Poisson's ratio, which can be tuned from positive to negative through a uniform soft deformation. We also prove that the bulk soft modes are associated with states of self-stress along the direction of zero strain during uniform soft deformation. The self-assembled transformable structures may act as mechanical metamaterials with potential applications in micromechanical engineering.

Drive-specific selection in multistable mechanical networks

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

An additive framework for kirigami design

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms.

Buckling versus unilateral constraint for a multistable metamaterial element

A structural element is designed and investigated, forming the basis for the development of an elastic multistable metamaterial. The leitmotif of the structural design is the implementation of a strut characterized by a bifurcation occurring at either vanishing tensile or compressive load. It is shown that buckling at null load leads to a mechanical equivalence with a unilateral constraint formulation, introducing shocks in dynamics. Towards a future analysis of the latter, the nonlinear quasi-static response is investigated, showing the multistable character of the structure, which may appear as bistable or tetrastable. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Continuum Field Theory for the Deformations of Planar Kirigami

Mechanical metamaterials exhibit exotic properties that emerge from the interactions of many nearly rigid building blocks. Determining these properties theoretically has remained an open challenge outside a few select examples. Here, for a large class of periodic and planar kirigami, we provide a coarse-graining rule linking the design of the panels and slits to the kirigami's macroscale deformations. The procedure gives a system of nonlinear partial differential equations expressing geometric compatibility of angle functions related to the motion of individual slits. Leveraging known solutions of the partial differential equations, we present an illuminating agreement between theory and experiment across kirigami designs. The results reveal a dichotomy of designs that deform with persistent versus decaying slit actuation, which we explain using the Poisson's ratio of the unit cell.

Theorem on the Compatibility of Spherical Kirigami Tessellations

We present a theorem on the compatibility upon deployment of kirigami tessellations restricted on a spherical surface with patterned slits forming freeform quadrilateral meshes. We show that the spherical kirigami tessellations have either one or two compatible states, i.e., there are at most two isolated strain-free configurations along the deployment path. The theorem further reveals that the rigid-to-floppy transition from spherical to planar kirigami tessellations is possible if and only if the slits form parallelogram voids along with vanishing Gaussian curvature, which is also confirmed by an energy analysis and simulations. On the application side, we show a design of bistable spherical domelike structure based on the theorem. Our study provides new insights into the rational design of morphable structures based on Euclidean and non-Euclidean geometries.