Calculation of Homogenized Mechanical Coefficients of Fiber-Reinforced Composite Using Finite Element Method

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Mechanics

Background:

• Determining composite material mechanical properties is crucial for design but often complex.
• Existing theoretical methods can be difficult to apply practically due to numerical challenges.
• Composite materials are increasingly utilized across various engineering applications.

Purpose of the Study:

• To obtain engineering elastic constants for composite materials.
• To apply theoretical results from homogenization theory.
• To provide a practical and accurate method for elastic constant determination.

Main Methods:

• Utilizing homogenization theory for theoretical underpinnings.
• Employing the finite element method (FEM) to calculate stress and strain fields.
• Applying the method of least squares to minimize errors and enhance FEM estimations.
• Analyzing multiple load cases for robust estimations.

Main Results:

• Successfully obtained engineering elastic constants for a transversely isotropic composite material.
• Demonstrated the effectiveness of combining homogenization theory with FEM.
• Validated the least squares method for refining FEM-derived elastic constants.
• Provided accurate elastic constants for a real-world composite case.

Conclusions:

• The proposed method accurately determines elastic constants for composite materials.
• The integration of homogenization theory, FEM, and least squares offers a powerful approach.
• This methodology is applicable to various composite structures and geometries.
• The findings contribute to more reliable composite material design and analysis.