Elastic Interfaces on Disordered Substrates: From Mean-Field Depinning to Yielding

Area of Science:

• Condensed matter physics
• Materials science
• Statistical mechanics

Background:

• Understanding the behavior of elastic manifolds in disordered systems is crucial for various physical phenomena.
• Depinning and yielding transitions are key concepts in describing the response of materials to external forces.

Purpose of the Study:

• To investigate the relationship between generalized long-range elasticity and the yielding transition in elastic manifolds.
• To explore how varying elastic properties, specifically the presence of zero modes, affect critical exponents.
• To determine the influence of microscopic pinning potentials on the flow curve and yielding behavior.

Main Methods:

• Development of a theoretical model for an elastic manifold driven on a disordered energy landscape.
• Incorporation of generalized long-range elasticity and systematic variation of the elastic kernel to include zero modes.
• Analysis of critical exponents and the Herschel-Buckley exponent of the flow curve.

Main Results:

• The model demonstrates a smooth interpolation between mean-field depinning and finite dimensional yielding as zero modes are introduced.
• Critical exponents of the system exhibit smooth changes during this interpolation.
• The Herschel-Buckley exponent is found to be dependent on the analytical form of the microscopic pinning potential.

Conclusions:

• The study suggests that yielding in finite dimensions can be described as a mean-field transition within the elastoplastic framework.
• The findings highlight the continuous nature of transitions in disordered elastic systems.
• The dependence of the Herschel-Buckley exponent on pinning potential offers insights into material flow characteristics.