Response evolution of mechanical metamaterials under architectural transformations

Abstract

Architectural transformations play a key role in the evolution of complex systems, from design algorithms for metamaterials to flow and plasticity of disordered media. Here, we develop a general framework for the evolution of the linear mechanical response of network structures under discrete architectural transformations via sequential removal and addition of elastic elements. We focus on a class of spatially complex metamaterials, consisting of triangular building blocks. Rotations of these building blocks, corresponding to removing and adding elastic elements, introduce (topological) architectural defects. We show that the metamaterials' states of self stress play a crucial role, and that the mutually exclusive self stress states between two different network architectures span the difference in their mechanical response. For our class of metamaterials, we identify a localized representation of these states of self stress, which allows us to capture the evolving response. We use our insights to understand the unusual stress-steering behaviour of topological defects.

arXiv commentMain text of 16 pages including 10 figures, supplementary information of 7 pages including 3 figures

References in corpus (28)

• Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
• Topological Boundary Modes in Isostatic Lattices
• On the feasibility of pentamode mechanical metamaterials
• Colloquium: Artificial spin ice: Designing and imaging magnetic frustration
• Programming Curvature using Origami Tessellations
• Topological modes bound to dislocations in mechanical metamaterials
• Geometric Frustration in Buckled Colloidal Monolayers
• Selective buckling via states of self-stress in topological metamaterials
• Bose-Einstein Condensation in a Plasmonic Lattice
• Topological mechanics of origami and kirigami
• Force network ensemble: a new approach to static granular matter
• Designing allostery-inspired response in mechanical networks
• Mechanical Weyl Modes in Topological Maxwell Lattices
• A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
• Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection
• Realizing Colloidal Artificial Ice on Arrays of Optical Traps
• Shape-morphing architected sheets with non-periodic cut patterns
• Non-affine response: jammed packings versus spring networks
• Engineering of frustration in colloidal artificial ices realized on microfeatured grooved lattices
• Rigidity Loss in Disordered Systems: Three Scenarios
• From confinement to deconfinement of magnetic monopoles in artificial rectangular spin ices
• Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
• Membrane undulations in a structured fluid: Universal dynamics at intermediate length and time scales
• Theory for the density of interacting quasi-localised modes in amorphous solids
• Linking microscopic and macroscopic response in disordered solids
• Stress Response of Granular Systems
• Attraction Controls the Inversion of Order by Disorder
• Statistical mechanics of glass transition in lattice molecule models

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• Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
• Combinatorial Design of Floppy Modes and Frustrated Loops in Metamaterials
• Breaking Mechanical Holography in Combinatorial Metamaterials