Computational Strategy for Analyzing Effective Properties of Random Composites-Part II: Elasticity.

Area of Science:

• Continuum Mechanics
• Materials Science
• Composite Materials Theory

Background:

• Traditional methods for calculating effective elastic constants in composites often lack explicit dependence on inclusion location.
• Previous numerical simulations were limited to fixed material constants and inclusion positions.
• The Representative Volume Element (RVE) concept, while useful, requires rigorous definition for accurate analysis.

Purpose of the Study:

• To develop a novel strategy for quantifying macroscopic properties of elastic plane composites.
• To derive new analytical and approximate formulas for effective elastic constants, explicitly showing dependence on inclusion location.
• To extend the analysis of dispersed random composites to two-dimensional elastic systems and revise the RVE concept.

Main Methods:

• Development of an analytical-numerical algorithm to derive expressions for effective constants.
• Rigorous demonstration that the RVE must be a fundamental domain of the plane torus (e.g., a periodicity parallelogram).
• Decomposition of effective elasticity tensors into geometrical and physical parts, enabling a novel computational methodology.

Main Results:

• New analytical and approximate formulas for effective elastic constants of dispersed random composites are presented.
• Explicit dependence of effective tensors on geometric probabilistic distributions of inclusions and computational protocols is demonstrated.
• Practical expressions for effective shear modulus, valid for all inclusion concentrations, are derived using resummation methods.

Conclusions:

• The revised RVE definition is crucial for obtaining correct effective constants in elastic composites.
• The proposed methodology allows for explicit analysis of how inclusion distribution affects composite properties.
• The study provides a framework for more accurate prediction of effective elastic properties in various composite materials.