Effect of boundary conditions on yield properties of human femoral trabecular bone

Abstract

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7-72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient [Formula: see text]. As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.

Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach

“…We also observed predominance of tensile solid phase strains in pure macroscopic shear, which is consistent with Sanyal et al (2012). Multilinear regressions suggest that uniaxial yield strains are not correlated with BV/TV and fabric (Matsuura et al, 2008; Morgan and Keaveny, 2001;Panyasantisuk et al, 2015). Only a mild dependence was found for the uniaxial compressive yield strains (R 2 ¼0.44, p-0), with a positive slope for density and a negative slope for fabric, which suggests that long trabeculae, i.e.…”

“…Our study considered yield points arising from 160 different load cases. Some recent studies have been limited to 17 load cases (Panyasantisuk et al, 2015;Wolfram et al, 2012). In order to compare our results we considered 17 strain cases similar to those in the cited studies.…”

“…The boundary conditions used to constrain the VE were kinematic uniform boundary conditions applied as described by Wang et al (2009). It is recognised that these boundary conditions provide an upper bound for trabecular bone stiffness and also for yield (Panyasantisuk et al, 2015;Wang et al, 2009). The simulations were run on a Cray XC30 supercomputer hosted by ARCHER, the UK National Supercomputing Service.…”

An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations

“…Thirteen different load cases, uniaxial tension in three directions, uniaxial compression in three directions, shear in three planes, triaxial tension and compression, and two multiaxial load cases are investigated to determine the strength surface in apparent stress space. The two multiaxial load cases are characterised by tensile loading in the 1 and 2 directions together with compression in 3 direction (load case 13) and compression in 1 and 2 directions as well as tension in 3 direction (load cases 16 in Panyasantisuk et al). The 13 load cases are applied to the same three trabecular bone samples using force‐controlled PMUBCs …”

“…Each cubic specimen was investigated under 17 different uniaxial and multiaxial load cases. A generalised anisotropic quadric yield criterion by Schwiedrzik et al was fitted to the results of μFE analyses in multiple studies . Panyasantisuk et al showed the effect of the applied boundary conditions in μFE simulations on the size of the yield surfaces in stress space.…”