A structural mathematical model for the viscoelastic anisotropic behaviour of trabecular bone

Area of Science:

• Biomechanics
• Materials Science
• Computational Bone Research

Background:

• Trabecular bone is a complex heterogeneous material with a distinct microstructure.
• Understanding the mechanical behavior of trabecular bone is crucial for diagnosing and treating bone diseases.

Purpose of the Study:

• To deduce a macroscopic constitutive equation for trabecular bone from its microstructural description.
• To develop a model that accounts for the elastic behavior of trabeculae and the Maxwell body behavior of the surrounding material.

Main Methods:

• A general theoretical approach to the mechanics of heterogeneous materials was employed.
• Trabeculae were modeled as elastic, and the inter-trabecular matrix as a Maxwell body.
• Tensorial internal variables were incorporated into the macroscopic constitutive equation.

Main Results:

• A macroscopic constitutive equation for trabecular bone was derived, incorporating material constants, volume fractions, and structural parameters.
• The model considers interconnected trabecular and matrix systems.
• Explicit formulas for transverse isotropy were derived, with potential for generalization to anisotropy.

Conclusions:

• The developed model provides a framework for understanding the mechanical response of trabecular bone based on its microstructural composition.
• The procedure for model parameter identification and a numerical example were demonstrated, validating the approach.