Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

Area of Science:

• Biomaterials Science
• Computational Mechanics
• Nanotechnology

Background:

• Cortical bone's mechanical properties are crucial for skeletal function.
• Understanding bone at the nanoscale is essential for developing effective treatments for bone diseases.
• Previous models often simplify bone's complex hierarchical structure.

Purpose of the Study:

• To develop and apply a hierarchical multiscale modeling scheme for analyzing cortical bone as a nanocomposite.
• To investigate the influence of varying mineral volume fractions on the elastic properties of cortical bone.
• To establish a framework for predicting the mechanical behavior of bone under diverse loading conditions.

Main Methods:

• A hierarchical multiscale modeling scheme was developed, incorporating macroscale and microscale boundary value problems.
• Homogenization techniques were employed to couple the different scales of analysis.
• A representative volume element (RVE) of the bone's microstructure was used to define the microscale problem.

Main Results:

• The study successfully analyzed the elastic properties of cortical bone by considering its nanoscale constituents.
• Elastic moduli, Poisson's ratios, and shear modulus were obtained for various mineral volume fractions.
• The model demonstrated the relationship between microstructural composition and macroscopic mechanical behavior.

Conclusions:

• The hierarchical multiscale modeling scheme provides a robust method for analyzing cortical bone as a nanocomposite.
• The findings highlight the significant impact of mineral content on the mechanical properties of bone.
• This approach is adaptable for modeling complex bone geometries and loading scenarios.