Multiscale Homogenization Techniques for TPMS Foam Material for Biomedical Structural Applications.

Area of Science:

• Computational mechanics
• Materials science
• Biomedical engineering

Background:

• Lattice structures, particularly triply periodic minimal surface (TPMS) based ones like gyroid and primitive surfaces, offer tunable mechanical properties.
• Analyzing these complex structures at full detail is computationally intensive, hindering design optimization.
• Multiscale techniques, such as homogenization, can overcome these limitations by providing effective material properties.

Purpose of the Study:

• To investigate the elastic and plastic properties of gyroid and primitive TPMS cellular structures using numerical homogenization.
• To develop accurate material laws for homogenized Young's modulus and yield stress.
• To demonstrate the application of these material laws in designing optimized, functionally graded biomedical implants, specifically a femoral stem, to mitigate stress shielding.

Main Methods:

• Numerical homogenization was employed to analyze the mechanical behavior of gyroid and primitive TPMS cellular structures.
• Material laws for effective elastic and plastic properties were derived from the homogenization results.
• These material laws were then used in an optimization analysis to design a functionally graded femoral stem.

Main Results:

• The derived material laws for homogenized Young's modulus and yield stress showed good agreement with existing experimental data.
• A functionally graded femoral stem design using a gyroid foam structure was developed.
• The optimized femoral stem exhibited stiffness comparable to trabecular bone, effectively minimizing stress shielding and reducing peak stresses within the implant.

Conclusions:

• Numerical homogenization is an effective multiscale technique for characterizing TPMS cellular structures, enabling the development of accurate material models.
• Functionally graded designs based on these models can significantly improve the performance of biomedical implants, such as femoral stems.
• The developed approach offers a pathway to creating implants that better integrate with bone tissue, reducing adverse effects like stress shielding.