Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites

Area of Science:

• Continuum Mechanics
• Materials Science
• Computational Mechanics

Background:

• Understanding material behavior across different scales is crucial for accurate predictions.
• Viscoelastic materials exhibit time- and frequency-dependent properties.
• Homogenization techniques bridge the gap between microscale and macroscale material responses.

Purpose of the Study:

• To investigate the scaling behavior of spatially random linear viscoelastic materials from the mesoscale to the macroscale.
• To develop frequency-dependent bounds for the representative volume element (RVE) response.
• To generalize the concept of scaling functions for viscoelastic composites.

Main Methods:

• Application of the Hill-Mandel homogenization condition adapted for viscoelasticity.
• Formulation of two stochastic initial-boundary value problems (kinematic and traction).
• Computational mechanics analysis of composites with planar random chessboard microstructures.

Main Results:

• Mesoscale bounds for RVE response were derived under homogenization conditions.
• Frequency and scale dependencies of these bounds were quantified.
• A complex-valued, frequency-dependent scaling function was established for viscoelastic composites.

Conclusions:

• The derived scaling function effectively describes the transition from mesoscale to macroscale for random viscoelastic materials.
• This function is general and depends primarily on microstructure and mesoscale properties.
• The findings extend previous work on linear elastic random composites to the viscoelastic regime.