Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / FEM Method: Trabecular bone cores were obtained from male human cadaveric T12 vertebrae. Bone voxels were directly converted from μCT to eight noded hexahedra. Isotropic and homogenous nonlinear damaging material properties (Fig. 2) were applied to each element. Axial loading was applied and a strain-based damageable elastic material property (Fig. 2) was applied iteratively. The strains within the trabecular bone cores were determined and used to apply the damaging criteria to five elements at a time; once the damaged elements were determined, their modulus was reduced. The model was rerun to determine the changes to the strain field and the next elements that would be damaged. Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Intrinsic Material Properties of the FEM: (a) Smooth dashed curve shows stress versus strain of a body with infinite sites to break, behaving initially linearly, followed by a smooth softening region and then failure. Jagged curves show the mechanical response of a body with 10, 5, 2 and 1 finite site(s) to break. (b) Idealization of a body with one site to break that breaks in two stages. A two stage intrinsic material model was used in this study. Damage was introduced in two stages (primary and secondary events) by reducing the intrinsic Young's Modulus (E i1 ) of elements exceeding chosen principal tensile strain values. Primary failure occurred at an intrinsic damage strain (ε i1 ), which reduced the modulus to the Intrinsic damaged material modulus (E i2 ) until loaded past the intrinsic rupture strain (ε i2 ), where a secondary failure occurs further reducing the modulus to E i35 = 100 MPa. W i,total the intrinsic toughness modulus was estimated as the area under the damage curve. Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Trabecular Bone Core Damage Site Prediction: 3D rendering of finite element model geometry obtained from Micro-CT imaging with damage sites resulting from axial compression with: E i2 = 500 MPa, ε i1 = 0.005, ε i2 = Left: Damage sites and deformation of the trabecular bone volume just prior to yield (0.002 offset method), ε a = Center: Damage sites and deformation of the trabecular bone volume after apparent yield (0.002 offset method). Right: Apparent axial stress-strain curve of the whole bone core. Red circle denotes the yield (0.002 offset method) point. The pre-yield (0.002 offset method) geometry (Left) clearly shows damage predicted during a nearly linear region of apparent deformation. Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Mechanical Input Contour Plot: Color maps depict (a) the normalized apparent toughness modulus (W a /E a ) and (b) normalized apparent yield strength (σ ay /E a ) resulting from FEA with ε i1 = 0.005, ε i2 (x-axis), and E i2 (y-axis). The color map illustrates the nonlinear relationship between the intrinsic damage material level properties and the apparent mechanical properties. The similarity of the plots for toughness and strength is consistent with the correlation found between the apparent yield strength (σ ay ) and apparent toughness modulus both experimentally and in the present computer modeling study. Additionally, the plots demonstrate that many combinations of intrinsic material level properties lead to effectively equivalent apparent mechanical properties. Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Stress-strain behavior of the FEM of trabecular bone cores at the apparent level with changes in the intrinsic material properties as a function of intrinsic damaged material modulus, E i2 (Left) and intrinsic rupture strain, ε i2 (Right). All models had the same geometry, intrinsic modulus, E i1 = 10 GPa, intrinsic damage strain, ε i1 = The mechanical response of the trabecular bone core to increasing either ε i2 or E i2 was nonlinear as increasing damage properties corresponded with increased apparent level behavior until ε i2 = 0.05 or E i2 = Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Comparison of damage quantity and distribution due to changes in intrinsic rupture strain (ε i2 ): four whole trabecular bone core models with E i1 = 10,000 MPa, ε i2 = 0.005, E i2 = 1100 MPa, and ε i2 as indicated. The damage depicted shows the first 10,000 damage events predicted within each model. The left most top panel is the only model shown with the bone. The sites of damage in the trabecular bone core model are shown in the other panels without the bone volume rendering, enabling all damage to be visualized. Both spatial clustering and temporal clustering (color) can be observed. The lower the failure strain the more clustering appears to occur, both spatially and temporally. The blue damage occurred first with red occurring at the end. The clustering of damage spatially and temporally does not entirely explain the differences in apparent toughness moduli. The ε i2 = 0.05 and ε i2 = 0.1 appear to have nearly identical damage distributions; however, the apparent toughness moduli (W a ) differed by 15%. The number of secondary failures was different across the four models. The number of primary and secondary damage events were both moderately negatively correlated with normalized apparent toughness modulus (W a /E a,init ; R 2 = 0.1 for primary and R 2 = 0.15 for secondary and R 2 = 0.19 cumulatively). Apparently, the small number of secondary failures 0.015% in the ε i2 = 0.05 model compared to the ε i2 = 0.1 model's 0% secondary failures has a large effect on the apparent level mechanical properties. Figure Legend:

Date of download: 6/22/2016 Copyright © ASME. All rights reserved. From: The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study J Biomech Eng. 2012;135(1): doi: / Damage volume versus normalized apparent toughness modulus (W a /E a,init ): The normalized apparent toughness modulus (W a /E a ) and the amount of primary and secondary damage are only loosely related. The top of a line segment is the total damage that occurred in a model, and the bottom of the line segment is the amount of primary damage that occurred in a model. Therefore, the length of the line is the amount of secondary damage that occurred. A general observation is that the larger values of apparent toughness associate with short line segments (i.e., small amounts of secondary damage). In statistical analysis, however, apparent toughness (W a /E a ) was weakly negatively related with primary (p < 0.001) and secondary damage volume in a linear multiple regression (R 2 model = 0.4 (p < 0.001), R 2 Primary|Secondary = 0.19 (p < 0.001), R 2 Secondary|Primary = 0.37 (p < 0.001)). Certain combinations of intrinsic material properties led to large amounts of damage without deteriorating apparent properties. Figure Legend: