Algorithms for a strain‐based plasticity criterion for bone

Pankaj, Pankaj; Donaldson, F.E.

doi:10.1002/cnm.2491

Cited by 19 publications

(26 citation statements)

References 45 publications

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“…Our study shows that the macroscopic yield surface of bone in normal strain space is fairly uniform across a wide range of samples; this confirms findings of previous research (Bayraktar et al, 2004;Lambers et al, 2014;Pankaj and Donaldson, 2013).…”

Section: Discussionsupporting

confidence: 92%

“…In recent years a consensus appears to be emerging that strainbased criteria are easier to apply as trabecular bone behaviour in this space is "more isotropic" and density independent than in stress space (Bayraktar et al, 2004;Chang et al, 1999;Pankaj and Donaldson, 2013). There is also now some evidence to suggest that failure of bone is strain-controlled rather than stress-controlled (Nalla et al, 2003) (Bayraktar et al, 2004;Sanyal et al, 2015;Wolfram et al, 2012).…”

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confidence: 93%

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

Levrero-Florencio

Margetts

Sales

et al. 2016

Journal of the Mechanical Behavior of Biomedical Materials

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Computational homogenisation approaches using high resolution images and finite element (FE) modelling have been extensively employed to evaluate the anisotropic elastic properties of trabecular bone. The aim of this study was to extend its application to characterise the macroscopic yield behaviour of trabecular bone. Twenty trabecular bone samples were scanned using a micro-computed tomography device, converted to voxelised FE meshes and subjected to 160 load cases each (to define a homogenised multiaxial yield surface which represents several possible strain combinations). Simulations were carried out using a parallel code developed in-house. The nonlinear algorithms included both geometrical and material nonlinearities. The study found that for tension-tension and compression-compression regimes in normal strain space, the yield strains have an isotropic behaviour. However, in the tension-compression quadrants, pure shear and combined normal-shear planes, the macroscopic strain norms at yield have a relatively large variation. Also, our treatment of clockwise and counter-clockwise shears as separate loading cases showed that the differences in these two directions cannot be ignored. A quadric yield surface, used to evaluate the goodness of fit, showed that an isotropic criterion adequately represents yield in strain space though errors with orthotropic and anisotropic criteria are slightly smaller. Consequently, although the isotropic yield surface presents itself as the most suitable assumption, it may not work well for all load cases. This work provides a comprehensive assessment of material symmetries of trabecular bone at the macroscale and describes in detail its macroscopic yield and its underlying microscopic mechanics.

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Section: Discussionsupporting

confidence: 92%

mentioning

confidence: 93%

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

Levrero-Florencio

Margetts

Sales

et al. 2016

Journal of the Mechanical Behavior of Biomedical Materials

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“…The bones were obtained from Meat Science Lab at the University of Illinois at Urbana-Champaign. The principal principal strain, 36 (D) cast iron, and (E) Mohr-Coulomb trabecular direction was estimated by performing a low-resolution micro-CT imaging. Subsequently, samples were cut out of femoral heads in the principal direction to obtain cylinder shapes with~8-mm height and~4-mm diameter, using the aspect ratio of 2:1 recommended for uniaxial compression tests.…”

Section: Sample Preparation and Experimental Proceduresmentioning

confidence: 99%

“…Different yield surfaces that are used for modeling plasticity of trabecular bone tissue: (A) von‐Mises, (B) Drucker‐Prager, (C) principal strain, (D) cast iron, and (E) Mohr‐Coulomb…”

Section: Introductionmentioning

confidence: 99%

Nonlinear micro‐CT based FE modeling of trabecular bone—Sensitivity of apparent response to tissue constitutive law and bone volume fraction

Sabet

Jin

Korić

et al. 2017

Numer Methods Biomed Eng

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In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

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“…Failure is typically modeled in micro-FE by changing the material properties of the bone elements according to a failure/yield criterion. This change in material properties has been based on plasticity (Donaldson et al 2008;Verhulp et al 2008a;Pankaj and Donaldson 2013) and nonlinear elasticity (Niebur et al 2000). However, the intrinsic material properties of bone depend on the complex organization of its basic constituents, namely a collagenous matrix with embedded platelike mineral crystals (Jager and Fratzl 2000).…”

Section: Introductionmentioning

confidence: 99%

Modeling microdamage behavior of cortical bone

Donaldson

Ruffoni

Schneider

et al. 2014

Biomech Model Mechanobiol

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Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.

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Algorithms for a strain‐based plasticity criterion for bone

Cited by 19 publications

References 45 publications

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

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

Nonlinear micro‐CT based FE modeling of trabecular bone—Sensitivity of apparent response to tissue constitutive law and bone volume fraction

Modeling microdamage behavior of cortical bone

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