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Emergent Elasticity in Amorphous Solids.

Jishnu N Nampoothiri1,2, Yinqiao Wang3, Kabir Ramola2

  • 1Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.

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Summary
This summary is machine-generated.

Amorphous solids like gels and tissues lack broken symmetry, unlike crystals. Their mechanical behavior is explained by a new generalized electromagnetism, revealing emergent elasticity from local constraints.

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Area of Science:

  • Physics
  • Materials Science
  • Soft Matter Physics

Background:

  • Conventional elasticity relies on broken symmetry, insufficient for amorphous solids (gels, jammed grains, tissues).
  • Athermal solids' mechanical response is governed by local mechanical equilibrium (force and torque balance).

Purpose of the Study:

  • To demonstrate that local mechanical constraints in amorphous solids map to a generalized electromagnetism.
  • To establish a new theoretical framework for understanding the elasticity of systems lacking broken symmetry.

Main Methods:

  • Developed a U(1) rank-2 symmetric tensor gauge theory of elasticity.
  • Mapped stress to electric displacement and forces to vector charges, analogous to fractonic phases.
  • Validated the theory using numerical simulations and experimental data.

Main Results:

  • The electrostatic limit of the generalized electromagnetism accurately captures amorphous solid elasticity.
  • Force chains in granular media are identified as subdimensional excitations of amorphous elasticity.
  • The theory provides a novel paradigm for emergent elasticity in systems without broken symmetry.

Conclusions:

  • Local mechanical constraints in amorphous solids can be mathematically described by generalized electromagnetism.
  • This framework offers a new perspective on elasticity, bridging concepts from condensed matter physics and electromagnetism.
  • The findings have implications for understanding diverse materials, from biological tissues to granular systems.