A consistent discretization via the finite radon transform for FFT-based computational micromechanics.

Area of Science:

• Computational micromechanics
• Homogenization methods
• Applied mathematics

Background:

• Periodic homogenization is crucial for material modeling.
• Existing methods like Moulinec-Suquet have limitations.
• The finite Radon transform offers a new perspective.

Purpose of the Study:

• To connect FFT-based micromechanics with the finite Radon transform.
• To develop a unified discretization framework.
• To extend Radon-based homogenization to small-strain mechanics.

Main Methods:

• Deriving multidimensional Radon series for periodic functions.
• Developing a general discretization framework using trigonometric polynomials.
• Combining Moulinec-Suquet and finite Radon approaches.

Main Results:

• A novel Radon framework is introduced.
• The framework ensures convergence under grid refinement.
• Exact representation of non-axis aligned laminates is achieved.

Conclusions:

• The proposed Radon framework enhances computational micromechanics.
• It offers advantages over existing discretization methods.
• Numerical examples validate the approach in small-strain mechanics.