Stress-stress correlations in two-dimensional amorphous and crystalline solids

Area of Science:

• Materials Science
• Condensed Matter Physics
• Solid Mechanics

Background:

• Elasticity theory (ET) traditionally explains stress-stress correlations in crystalline solids.
• Amorphous solids, with their disordered structures, present challenges for traditional ET frameworks.
• Tensor gauge theories have emerged as a potential approach for disordered solids.

Purpose of the Study:

• To investigate emergent elasticity and stress-stress correlations in 2D amorphous and crystalline solids.
• To evaluate the applicability of canonical elasticity theory to disordered materials.
• To compare the behavior of amorphous solids with crystalline solids using experimental and simulation data.

Main Methods:

• Application of a canonical elasticity theory (ET) approach.
• Analysis of experimental and simulation data for 2D solids.
• Examination of static stress-stress correlations and pinch-point singularities.

Main Results:

• 2D disordered solids exhibit static stress-stress correlations indistinguishable from 2D isotropic crystalline solids.
• Standard elasticity theory accurately predicts the stress response of these disordered solids.
• Pinch-point singularities are not exclusive to amorphous solids, appearing in crystalline solids as well.

Conclusions:

• The static stress-stress correlations in 2D amorphous solids are universally predictable using conventional elasticity theory.
• The findings challenge the notion that disordered solids require entirely new theoretical frameworks for elasticity.
• This work reinforces the universality of static stress-stress correlations across different material structures.