Construction of the effective plastic yield surfaces of vertebral trabecular bone under twisting and bending moments stresses using a 3D microstructural model

Abstract

Trabecular bone experiences complex multiaxial loads which can lead to entire bone fracture. The available knowledge of the failure properties of trabecular under multiaxial states of stress is quite limited, especially under bending and twisting moment stresses. Analytical models of the mechanical response of trabecular bone based on microstructural models can significantly enhance our understanding of multiaxial failure behavior under such loadings. For this purpose, plastic yield surfaces are derived for lattice-like models of the trabecular bone structure with a relatively high effective density, such that failure occurs by full plastic flow. The asymptotic discrete homogenization approach is involved to construct the plastic collapse surfaces of the periodic 3D rod-like architecture of vertebral bone in micropolar couple stress space incorporating natural anisotropy of bone. Both in-plane and out-of-plane bending couple stress states are considered in addition to torsional couple stresses. A plastic yield criterion is adopted to address general bending and torsional couple loadings, accounting for combined cell wall bone microstructure bending and torsion. The criterion for full plastic yielding is micromechanically motivated and relies on the calculation of the microscopic couple stresses (or micromoments) that are linked to the homogenized curvatures. The plastic yield surface is associated to a complete plasticization of the trabecular strut section. Additionally, since the effective bone density is the most important factor affecting the failure behavior of bone, the plastic strengths of vertebral bone are obtained in terms of the relative density to provide insights about the impact of bone relative density on the plastic collapse conditions. The vertebral plastic failure domains due to torsional and bending couple stresses are related to the relative density, expressed in terms of the micro-architecture parameters, itself changing with age.

Sub-trabecular strain evolution in human trabecular bone

“…It is not granted that the findings from single trabeculae are generalizable to the trabecular network structure level, which experiences large-deformation, bending, and buckling under loading. In this context, novel computational models have been developed to investigate this interconnection 22,23 , but they lack experimental verification at the correct scale.…”