Efficient materially nonlinear FE solver for simulations of trabecular bone failure.

Area of Science:

• Biomechanics
• Materials Science
• Computational Modeling

Background:

• Linear solvers are efficient for large-scale simulations but often lack the capacity to model complex nonlinear material behaviors.
• Trabecular bone exhibits intricate nonlinear material properties, including damage-based degradation and fracture, which are crucial for understanding its mechanical response and failure mechanisms.

Purpose of the Study:

• To extend an efficient large-scale linear solver to incorporate nonlinear material behavior, specifically for modeling damage-based tissue degradation and fracture in trabecular bone.
• To validate the enhanced framework by applying it to experimental data from trabecular biopsies and to investigate the failure mechanisms of trabecular bone.

Main Methods:

• An efficient large-scale linear solver was modified to include a material model featuring damage-based tissue degradation and fracture.
• The enhanced solver was applied to 20 trabecular biopsies using a specified mesh resolution.
• Material parameters were calibrated using two biopsies against axial tension and compression experimental data.

Main Results:

• The enhanced solver maintained good parallel performance and a low memory footprint.
• Simulations demonstrated excellent correlation with experimental data for maximum apparent stress ($R^2$ = 0.93).
• The development of local damage regions was observed, leading to the proposal of a novel elasticity limit lower than the 0.2% yield point.

Conclusions:

• The extended solver accurately captures the nonlinear behavior of trabecular bone, including damage and fracture.
• Observed systematic differences in yield behavior under tension and compression suggest that damage distributions provide deeper insight into trabecular bone failure mechanisms.
• The proposed elasticity limit offers a new metric for characterizing bone material properties.