Combinatorial Design of Floppy Modes and Frustrated Loops in Metamaterials
arXiv:2503.12867 · doi:10.1103/nqgr-tfb1
Abstract
Metamaterials are a promising platform for a range of applications, from shock absorption to mechanical computing. These functionalities typically rely on floppy modes or mechanically frustrated loops, both of which are difficult to design. In particular, how to design multiple modes or loops with target deformations remains an open problem. We introduce a combinatorial approach that allows us to create an arbitrarily large number of floppy modes and frustrated loops. The design freedom of the mode shapes enables us to easily introduce kinematic incompatibility to turn them into frustrated loops. We demonstrate that floppy modes can be sequentially buckled by using a specific instance of elastoplastic buckling. We utilize our combinatorial floppy chains and frustrated loops to achieve matrix-vector multiplication in materia. Our findings bring about new principles for the design and the use of floppiness and geometric frustration in soft matter and metamaterials.
arXiv commentVideos available at https://shokef.sites.tau.ac.il/publications
References in corpus (36)
- Topological Boundary Modes in Isostatic Lattices
- Modeling semiflexible polymer networks
- Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
- Combinatorial Design of Textured Mechanical Metamaterials
- Static non-reciprocity in mechanical metamaterials
- Topological modes bound to dislocations in mechanical metamaterials
- Geometric origin of excess low-frequency vibrational modes in amorphous solids
- Coherent phonon manipulation in coupled mechanical resonators
- Criticality and isostaticity in fiber networks
- Multi-step self-guided pathways for shape-changing metamaterials
- Designing allostery-inspired response in mechanical networks
- Low-frequency vibrations of soft colloidal glasses
- Mechanical Weyl Modes in Topological Maxwell Lattices
- A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
- Density of states of colloidal glasses
- Intrinsically polar elastic metamaterials
- Automated discovery of reprogrammable nonlinear dynamic metamaterials
- Counting and Sequential Information Processing in Mechanical Metamaterials
- Topological defects produce exotic mechanics in complex metamaterials
- Conformal Elasticity of Mechanism-Based Metamaterials
- Topological edge floppy modes in disordered fiber networks
- Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control
- Emergent Disorder and Mechanical Memory in Periodic Metamaterials
- Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials
- Topological mechanics in quasicrystals
- Pneumatic Computers for Embedded Control of Microfluidics
- Response evolution of mechanical metamaterials under architectural transformations
- Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
- Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
- Embodying mechano-fluidic memory in soft machines to program behaviors upon interactions
- Robustness of stress focusing in soft lattices under topology-switching deformation
- Emergent Nonlocal Combinatorial Design Rules for Multimodal Metamaterials
- Architecting mechanisms of damage in topological metamaterials
- A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
- Breaking Mechanical Holography in Combinatorial Metamaterials
- Defect Positioning in Combinatorial Metamaterials