On the Finite Element Implementation of Functionally Graded Materials

Area of Science:

• Materials Science
• Computational Mechanics
• Solid Mechanics

Background:

• Functionally Graded Materials (FGMs) exhibit spatially varying properties, posing challenges for numerical simulation.
• Accurate implementation of these graded properties is crucial for predicting material behavior under load.
• Existing commercial finite element software often has limitations in handling FGMs.

Purpose of the Study:

• To numerically implement and compare two common schemes for functionally graded properties within the finite element method.
• To develop a user subroutine for ABAQUS to enhance the implementation of FGMs.
• To assess the suitability of different FGMs implementation approaches for fracture analysis.

Main Methods:

• Investigated nodal-based and Gauss integration point-based gradation schemes for FGMs.
• Solved benchmark boundary value problems with analytical solutions to validate formulations.
• Developed and implemented a user subroutine for the ABAQUS finite element package.

Main Results:

• Significant differences were observed between nodal-based and Gauss integration point-based gradation schemes.
• The study details the nature of these differences through analysis of boundary value problems.
• A new ABAQUS subroutine was successfully developed to address limitations in current FGM implementation.

Conclusions:

• Element-based formulations for FGMs are essential for reliable numerical analysis.
• The developed ABAQUS subroutine offers a more robust approach for implementing FGMs.
• Accurate numerical modeling of FGMs is critical for applications such as fracture assessment.