Thin Elastic Bodies

An elastic solid is equipped with a well-defined reference metric tensor - a set of distances between each two neighboring material elements which minimizes the energy of local interactions. There is no a priori reason for this geometry to be immersible in the geometry of ambient space, and therefore there may be no physical configuration in which the body is free of elastic stresses. Thin elastic bodies are of special interest, since they can significantly reduce residual stresses with modes of bending and twisting that may exhibit interesting patterns at multiple length scales. These patterns are closely related to the geometric embedding problem involving the reference and ambient (including boundary) geometries.

Related Papers

  • Internal Stresses Lead to Net Forces and Torques on Extended Elastic Bodies
    H. Aharoni, J. M. Kolinski, M. Moshe, I. Meirzada & E. Sharon, Phys. Rev. Lett. 117, 124101 (2016)
  • Emergence of Spontaneous Twist and Curvature in non-Euclidean Rods: Application to Erodium Plant Cells
    H. Aharoni, Y. Abraham, R. Elbaum, E. Sharon & R. Kupferman, Phys. Rev. Lett. 108, 238106 (2012)
  • Twist Renormalization in Chiral Rod Assemblies
    A. Haddad, H. Aharoni, R. Kupferman, E. Sharon, B. Kahr & E. Efrati (In preparation)

Liquid Crystals

Liquid crystals are found midway between liquids and solids in terms of their local symmetry and order. While they cannot be attributed a complete reference metric tensor as in solids, certain aspects of the local geometry must be maintained implying a reference geometry in some weaker sense. This gives rise to geometric frustration between local geometric constraints and the geometry of ambient space or topological constraints on defects in the liquid crystalline structure, which may lead to complex solutions and patterns. The full topological classification of defects and defect interactions, as well as the ground state geometry, elasticity, dynamics, and stability of these topologically distinct states, is in the heart of understanding the behavior of liquid crystalline systems.

Related Papers

  • Composite Dislocations in Smectic Liquid Crystals
    H. Aharoni, T. Machon & R.D. Kamien, Phys. Rev. Lett. 118, 257801 (2017)
  • Singularity Theory and the Structure of Defects in Smectics
    T. Machon, H. Aharoni, Y. Hu & R.D. Kamien (In preparation)

Liquid Crystals and Thin Elastic Bodies

Theories of liquid crystals and solid elasticity come together in various ways. Some elastic materials, such as nematic elastomers and glasses, have reference metric tensors which are coupled to liquid crystalline order of their mesogenic constituents. This order can be extrinsically controlled by various ambient conditions, giving rise to a class of programmable shape-shifting objects. In addition, liquid crystal theories are general mathematical descriptions of continua with some partial translational and rotational order. As such, they capture essential elements of patterns formed in various continuum systems, specifically in thin elastic solids.

Related Papers

  • Geometry of Thin Nematic Elastomer Sheets
    H. Aharoni, E. Sharon & R. Kupferman, Phys. Rev. Lett. 113, 257801 (2014)
  • Inverse Design of Arbitrary Surfaces with Thin Nematic Elastomer Sheets
    H. Aharoni, Y. Xia, X. Zhang, R.D. Kamien & S. Yang (In preparation)
  • The Smectic Order of Wrinkles
    H. Aharoni, D. V. Todorova, O. Albarrán, L. Goehring, R. D. Kamien & E. Katifori, Nat. Commun. 8, 15809 (2017)

More

I have a broad interest in soft matter problems that are governed by fundamental principles of geometry and topology. At one end of this spectrum are purely theoretical questions that involve exotic geometries of both the material and embedding space, as well as other physical and mathematical curiosities. At the other end is the application of principles and soft matter theories (solid elasticity, liquid crystal theory, fluid dynamics etc.) to the understanding of everyday problems and experimental observations.

Related Papers

  • Shape Selection in Chiral Ribbons: from Seed Pods to Supramolecular Assemblies
    S. Armon, H. Aharoni, M. Moshe & E. Sharon, Soft Matter 10, 2733-2740 (2014)
  • Growth and Nonlinear Response of Driven Water Bells
    J. M. Kolinski, H. Aharoni, J. Fineberg & E. Sharon, Phys. Rev. Fluids 2, 42401 (2017)
  • Topological Swimming in Locally Euclidean Spaces
    H. Aharoni & R.A. Mosna (In preparation)