Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Area of Science:

• Biomechanics
• Materials Science
• Orthopedics

Background:

• Micro-finite element models are used to study trabecular bone properties.
• Macroscopic elastic properties of bone are understood, but yield behavior is not.
• Understanding bone yield is crucial for predicting bone strength and implant stability.

Purpose of the Study:

• To investigate the effect of solid phase yield criteria on macroscopic yield of trabecular bone.
• To compare the Drucker-Prager and eccentric-ellipsoid yield criteria.
• To analyze the influence of bone microstructure and density on yield behavior.

Main Methods:

• Micro-finite element models were used.
• Three trabecular bone samples with varying densities were analyzed.
• Samples were subjected to diverse apparent load cases.
• Two solid phase yield criteria (Drucker-Prager and eccentric-ellipsoid) were applied.

Main Results:

• The choice of yield criterion had minimal impact on macroscopic yield strains for most load cases.
• Compression-dominated loading cases showed significantly higher yield strains with the Drucker-Prager criterion.
• Higher bone density amplified the differences between the two yield criteria.

Conclusions:

• The solid phase yield criterion plays a role in trabecular bone's macroscopic yield behavior.
• The Drucker-Prager criterion may overestimate yield strength in compression-dominated scenarios.
• This study provides insights into trabecular bone mechanics for diverse microstructures and loading conditions.