# Achievement

## New framework to explain shear rigidity in materials

### Project

IGERT: Geometry and Dynamics -- Integrated Education in the Mathematical Sciences

### University

Brandeis University

(Waltham, MA)

### PI

## Research Achievements

### New framework to explain shear rigidity in materials

Dapeng Bi, Bulbul Chakraborty, and Sumantra Sarkar constructed a new framework to explain shear rigidity in materials such as dry sand. In equilibrium statistical mechanics, shear rigidity arises from broken translational invariance. How materials without attractive interactions develop correlations leading to this broken symmetry, in the absence of thermal fluctuations, is a long-standing puzzle. Bi et al: (a) established a statistical ensemble for granular solids created through shearing or compression, and (b) used this ensemble and the constraints of mechanical equilibrium to demonstrate the emergence of broken translational invariance in the space of forces, not positions of grains. This type of broken symmetry is ordered states in quantum matter, and the work was partly inspired by talks by an IGERT seminar speaker from the quantum information community. Part (a) will appear in Europhysics Letters, and part (b) has been submitted to Physical Review Letters.

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