Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of 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 two-dimensional (2D) 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 postinstability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical 2D structures. Possible applications of the tools developed in this work for the study of ordered and disordered 2D porous elastic metamaterials are discussed.
|Original language||American English|
|Number of pages||8|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - 12 May 2020|
Bibliographical noteFunding Information:
ACKNOWLEDGMENTS. M.M. acknowledges useful discussion with David R. Nelson, Mark J. Bowick, and Eran Sharon. Y.B.-S. acknowledges support from the James S. McDonnell postdoctoral fellowship for the study of complex systems. M.M. acknowledges support from the Israel Science Foundation (Grant 1441/19). K.B. acknowledges support from NSF Grants DMR-1420570 and DMR-1922321.
© 2020 National Academy of Sciences. All rights reserved.
- Elastic charges
- Mechanical metamaterials
- Nonlinear elasticity