PSI - Issue 37

Ekaterina Smotrova et al. / Procedia Structural Integrity 37 (2022) 257–262 E. Smotrova et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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To build a unit cell for FE simulations, a trabecular-bone compartment was separated from other tissues (soft tissues, cortical bone and bone marrow) in the scans using thresholding of grayscale values. Scans of a phantom provided by the manufacturer were used to determine a relationship between grayscale values and BMD. Trabecular bone was segmented semi-automatically based on a fixed threshold value (350 mgHA/cm 3 ) and reconstructed using Materialise Mimics Innovation Suite 21.0 (Materialise, Leuven, Belgium). As a result of separation, 3.9 mm x 4.1 mm x 4.0 mm voxelized lattice was extracted from the scans (Fig. 1) representing trabecular bone of a medial anatomic region of the distal tibia. The intertrabecular (marrow) constituent had a negligible effect on the overall mechanical competence of the trabecular bone material and, therefore, was not included in the model. The bone volume fraction of the resulting model was 50%.

Fig. 1 Trabecular lattice extracted from HR-pQCT scan

2.2. Model development

The model of trabecular unit cell was meshed using dual marching cubes algorithm, according to Cohen-Or et al. (2000), with a global mesh size of 0.04 mm using Mathematica software (Wolfram Research, Inc., Champaign, IL, USA). Meshing resulted in approximately 750,000 tetrahedral elements of type C3D4. The material used in the model represented bone compartment of trabecular bone and was modelled as isotropic elastoplastic material. The elastic and plastic material parameters were assigned based on the data on mechanical properties obtained for individual trabeculae: Young's modulus = 7.6 GPa, yield stress = 59 MPa, ultimate tensile stress = 138 MPa (Frank et al. 2017), Poisson's ratio = 0.3 (Gillard et al. 2014). The stress-strain curve of the resulting material model is shown in Fig. 2. Few FEA studies attempted to model trabecular bone as either ductile or brittle material for determining its post yield behavior (Harrison et al. 2013, Nawathe et al. 2013). There is currently no consensus about the most appropriate material formulation. Hence, this study implemented both ductile and brittle material models aiming to investigate the difference in modelling results for the onset of microdamage and failure in human trabecular bone. The brittle material was modelled as purely elastic, with the onset of fracture corresponding to exceeding of the ultimate tensile strength of the material by the maximum principal stress. The ductile material was modelled as elastoplastic, with the onset of fracture corresponding to exceeding of the yield stress of the material by the effective (von Mises) stress. The brittle elastic and ductile elastoplastic models of trabecular unit cell were subjected to uniform displacement of ±0.03 mm perpendicularly to the top surface of the model to apply tensile and compressive loading regimes. The bottom surface of the model was rigidly fixed. Finite-element simulations were implemented with Abaqus v.2017