Fractional viscoelastic models for power-law materials

Area of Science:

• Materials Science
• Rheology
• Applied Mathematics

Background:

• Soft materials exhibit complex viscoelastic behavior due to diverse internal timescales.
• Power-law responses are common but challenging to model comprehensively.
• Fractional calculus presents a powerful, yet underutilized, mathematical framework for rheological analysis.

Purpose of the Study:

• To provide an accessible overview of fractional calculus models for viscoelasticity.
• To demonstrate the utility of fractional models in unifying the characterization of power-law materials.
• To encourage wider adoption of fractional calculus in soft matter research.

Main Methods:

• Review of existing literature on fractional calculus in viscoelasticity.
• Explanation of fractional operators and their application to soft material models.
• Analysis of rheological data using a consistent fractional calculus framework.

Main Results:

• Fractional calculus provides a unified mathematical framework for describing power-law viscoelasticity.
• The models effectively capture the broad distribution of timescales in soft materials.
• A consistent approach facilitates better classification and understanding of material responses.

Conclusions:

• Fractional calculus is a valuable tool for rheological characterization of soft materials.
• Simplified explanations can increase the accessibility and application of these models.
• Wider adoption can lead to improved understanding and classification of complex material behaviors.