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Tensor electromagnetism and emergent elasticity in jammed solids.
Jishnu N Nampoothiri1,2, Michael D'Eon1, Kabir Ramola2
1Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
Physical Review. E
|January 21, 2023
Summary
We developed a new theory for jammed solids, revealing emergent elasticity through a U(1) tensor electromagnetism. This framework explains how amorphous materials sustain shear, linking mechanical properties to electromagnetic responses.
Area of Science:
- Physics
- Materials Science
- Condensed Matter Physics
Background:
- Disordered, jammed solids present challenges in understanding shear stress transmission.
- Nonperiodic networks in jammed solids behave like fluids but sustain shear.
- Open questions remain regarding the mechanical response of amorphous materials.
Purpose of the Study:
- To present a stress-only theory for emergent elasticity in nonthermal amorphous granular solids.
- To establish a connection between grain-level constraints and macroscopic mechanical behavior.
- To explore the relationship between amorphous elasticity and tensor electromagnetism.
Main Methods:
- Formulated a theory based on force and torque balance constraints on individual grains.
- Developed an emergent U(1) tensor electromagnetism from grain-level constraints.
- Mapped mechanical responses to static dielectric responses and simulated frictionless granular packings.
Main Results:
- Grain-level constraints lead to Gauss's law of emergent U(1) tensor electromagnetism.
- Mechanical response directly maps to the static dielectric response.
- Polarizability of the medium corresponds to emergent elastic moduli.
- External forces act as electric charges, and momentum density sources magnetic fields.
Conclusions:
- The theory successfully accounts for the mechanical response of jammed solids.
- Theoretical predictions for stress-stress correlations and responses are validated by simulations.
- The U(1) tensor electromagnetism provides a novel framework for understanding amorphous elasticity.
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