A study of the stress-strain state of cancellous bone tissue under uniaxial compression

In this paper, the stress-strain state of model fragments of cancellous bone tissue under uniaxial compression is studied. The architecture of model cancellous tissue fragments mimics that of natural bone fragments. The model fragments of cancellous bone tissue are represented by a set of trabecular nodes, including the central element and the principal and secondary trabeculae of the certain length, thickness, and mineral content. The study of the von Mises stress distribution and normal strains shows that for the samples with short principal trabeculae, the largest normal strains and von Mises stresses are localized in the surface layers of the principal trabeculae. These characteristics are uniformly distributed over the thickness of the middle part of the principal trabeculae and decrease in their values with an increase in the principal trabecula length. It is revealed that with an increase in the length of the cancellous bone principal trabeculae, the effective longitudinal modulus of elasticity of the bone sample decreases according to a power law. The interaction between the principal and secondary trabeculae determines the deformation response of the bone samples in three mutually perpendicular directions under axial compression, which variously manifests itself depending on structural parameters and mass fraction of the trabeculae minerals.