Odd Mechanical Screening: A Continuum Mechanics of Disordered Solids

I present a continuum theory of odd mechanical screening, which generalizes classical elasticity to capture anomalous mechanical responses observed in disordered granular matter. The theory introduces an odd constitutive relation linking the displacement field with an induced dislocation field, encapsulating two distinct length scales—odd and even—absent from conventional theories of solids. These novel length scales enable precise predictions that align with experimental measurements of 2D granular models.

While the theory draws analogies to electrostatics, I will show that mechanical screening in disordered solids is fundamentally richer, exhibiting multiple screening regimes, even in the linear regime. Furthermore, the results suggest a potential link between the celebrated hexatic phase in two dimensional crystal melting and the behavior of nearly jammed disordered granular materials, opening new avenues for understanding phase transitions in complex solids.