Odd elasticity

By Colin Scheibner, Anton Souslov, D. Banerjee, Piotr Surówka, William T. M. Irvine, V. Vitelli. Nature Physics, 2019

343 citations recorded by the source corpus.

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non-conservative microscopic interactions. These active moduli enter the antisymmetric (or odd) part of the static elastic modulus tensor and quantify the amount of work extracted along quasistatic strain cycles. In two-dimensional isotropic media, two chiral odd-elastic moduli emerge in addition to the bulk and shear moduli. We discuss microscopic realizations that include networks of Hookean springs augmented with active transverse forces and non-reciprocal active hinges. Using coarse-grained microscopic models, numerical simulations and continuum equations, we uncover phenomena ranging from auxetic behaviour induced by odd moduli to elastic wave propagation in overdamped media enabled by self-sustained active strain cycles. Our work sheds light on the non-Hermitian mechanics of two- and three-dimensional active solids that conserve linear momentum but exhibit a non-reciprocal linear response. Active, non-conservative interactions can give rise to elastic moduli that are forbidden in equilibrium and enter the antisymmetric part of the stiffness tensor. The resulting solids function as distributed elastic engines that can perform work on their surroundings through quasistatic strain cycles.

Subfields: Cell Biology, Condensed Matter Physics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/211d6a623a19c8b6a61ac8ecb5857c2594a41978

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Citations in the corpus

Topological active matter (2020, background): “An active example is given by a solid that has bonds that are described by the non-conservative force law , where r ̂ ( ̂ φ ) is a unit vector pointing along (transverse to) the bond vector, δ r is the change in length of the bond, and k and k a are spring constants (part c of the figure) 225 .”
Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model (2020, background): “Such exceptional points have recently been encountered in other active matter systems such as active solids with odd elasticity [43].”
Symmetry, Thermodynamics, and Topology in Active Matter (2021, background): “The role of nonreciprocity in mesoscale effective interactions has also been highlighted in the context of the elasticity of materials where the interactions among the individual constituents are non-conservative [137].”