Odd Mechanical Screening: From Metamaterial to Continuum Mechanics of Disordered Solids

Holes in elastic metamaterials, defects in 2D curved crystals, localized plastic deformations in amorphous solids and T1 transitions in epithelial tissue, are typical realizations of stress-relaxation mechanisms in different solid-like structures, interpreted as mechanical screening.

In this talk I will present a mechanical screening theory that generalizes classical theories of solids, and introduces new moduli that are missing from the classical theories. Contrary to its electrostatic analog, the screening theory in solids is richer even in the linear case, with multiple screening regimes, predicting qualitatively new mechanical responses. 

The theory is tested in different physical systems, including disordered granular solids that do not have a continuous mechanical description. These materials are shown to violate energy conservation and are best described by Odd-Screening: a screening model that does not derive from an energy function. Experiments reveal a mechanical response that is strictly different from classical solid theory and is completely consistent with our mechanical-screening theory. Finally, I will discuss the relevance of this theory to 3D solids and a new Hexatic-like state in 3D matter.