Wave Propagation Analysis in the Homogenized Second-Gradient Medium: A Direct and Inverse Approach

Area of Science:

• Continuum Mechanics
• Materials Science
• Computational Mechanics

Background:

• Classical Cauchy elasticity does not capture size and microstructure effects in materials.
• Homogenization methods are crucial for understanding composite material behavior.
• Strain gradient elasticity offers a more comprehensive constitutive model.

Purpose of the Study:

• To develop a homogenization method for 2D periodic composite materials using second-order gradient continuum models.
• To incorporate strain gradient effects into constitutive laws for enhanced accuracy.
• To investigate wave propagation in these composites and the influence of microstructural features.

Main Methods:

• Formulation of a constitutive law using a variational approach and Hill's macro-homogeneity condition.
• Calculation of effective strain gradient moduli for composites with internal length effects.
• Development of an inverse homogenization method to determine local material properties.
• Analysis of longitudinal and shear wave propagation, considering inclusion shape, volume fraction, and property contrast.

Main Results:

• The proposed method successfully captures elastic size and microstructure effects.
• Effective strain gradient moduli were computed, validating the approach through strain energy calculations.
• The inverse homogenization method showed good agreement with literature data.
• Elliptic inclusions slightly increased wave propagation speeds for both longitudinal and shear waves.
• Property contrast significantly influenced wave dispersion.

Conclusions:

• The developed homogenization framework effectively models 2D composite materials with strain gradient effects.
• The study provides insights into the impact of microstructural parameters on wave propagation.
• This work offers a robust method for analyzing complex composite behaviors and predicting their mechanical responses.