TY - JOUR
T1 - Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials
AU - Bar-Sinai, Yohai
AU - Librandi, Gabriele
AU - Bertoldi, Katia
AU - Moshe, Michael
N1 - Publisher Copyright:
© 2020 National Academy of Sciences. All rights reserved.
PY - 2020/5/12
Y1 - 2020/5/12
N2 - 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.
AB - 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.
KW - Elastic charges
KW - Mechanical metamaterials
KW - Nonlinear elasticity
UR - http://www.scopus.com/inward/record.url?scp=85084440432&partnerID=8YFLogxK
U2 - 10.1073/pnas.1920237117
DO - 10.1073/pnas.1920237117
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C2 - 32350137
AN - SCOPUS:85084440432
SN - 0027-8424
VL - 117
SP - 10195
EP - 10202
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 19
ER -