Finite element analysis of a three-dimensional open-celled model for trabecular bone

Area of Science:

• Materials Science
• Biomechanics
• Solid Mechanics

Background:

• Subchondral trabecular bone and porous foams share structural similarities.
• Idealized models are crucial for understanding complex material behaviors.
• Previous models may not fully capture the mechanical response of these heterogeneous structures.

Purpose of the Study:

• To develop an idealized 3D model of porous materials with cubic symmetry.
• To determine the elastic constants of an equivalent homogeneous material.
• To validate the model by comparing predictions with experimental data for bone and foam.

Main Methods:

• Constructed a 3D model using regular arrays of cubic unit cells with body-centered spherical voids.
• Applied uniaxial compressive and shear strain to the model.
• Calculated the tensor of elastic constants for the equivalent homogeneous material.

Main Results:

• The model successfully predicted the elastic constants for a cubic symmetric solid.
• The predicted elastic modulus aligned with experimental values for bovine trabecular bone.
• Model predictions were comparable to literature values for open-celled latex rubber foam.

Conclusions:

• The idealized cubic unit cell model effectively represents the mechanical behavior of subchondral bone and porous foams.
• This modeling approach provides a reliable method for predicting the elastic properties of such materials.
• The findings support the use of this model in biomechanical and materials science research.