Geometric charges and nonlinear elasticity of soft metamaterials

Abstract

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability and aspects of the post-instability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical structures. Possible applications of the tools developed in this work for the study of ordered and disordered porous mechanical metamaterials are discussed.

12 pages, 5 figures

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Cited by in corpus (11)

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• Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions
• Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors
• Wavenumber-space band clipping in nonlinear periodic structures
• Geometric Theory of Mechanical Screening in two-dimensional solids
• Stable and unstable trajectories in a dipolar chain
• Elastic multipole method for describing linear deformation of infinite 2D solid structures with circular holes and inclusions
• Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions
• Breaking Mechanical Holography in Combinatorial Metamaterials
• Nonlinear extension of Kolosov-Muskhelishvili stress function formalism
• Defect Positioning in Combinatorial Metamaterials