Geometric theory of mechanical screening in two-dimensional solids

Area of Science:

• Solid mechanics
• Materials science
• Condensed matter physics

Background:

• Stress relaxation in solids occurs via various mechanisms, including holes in mechanical metamaterials, plastic events in amorphous solids, and dislocations in hexatic matter.
• These diverse relaxation modes share a common quadrupolar nature, fundamentally enabling stress screening within solid materials.

Purpose of the Study:

• To propose a novel geometric theory for stress screening in generalized solids based on the quadrupolar nature of local stress relaxation modes.
• To establish an analogy between stress screening in solids and electrostatic screening phenomena.

Main Methods:

• Development of a geometric theory for stress screening.
• Introduction of a hierarchy of screening modes, each defined by internal length scales.
• Drawing parallels with established electrostatic screening theories like dielectrics and Debye-Hückel theory.

Main Results:

• The proposed theory provides a unified framework for understanding stress screening across different solid materials and relaxation mechanisms.
• The theory incorporates a hierarchy of screening modes, characterized by distinct internal length scales.
• The formalism suggests a potential redefinition of the hexatic phase based on mechanical properties, not just structural ones.

Conclusions:

• Local stress relaxation modes in solids are fundamentally quadrupolar, forming the basis for stress screening.
• The geometric theory offers a new perspective on stress screening, analogous to electrostatic phenomena.
• The study proposes that the hexatic phase can be characterized by mechanical properties and may be present in amorphous materials.