Calculation of the critical energy release rate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>of the cement line in cortical bone combining experimental tests and finite element models

Giner, Eugenio; Belda, Ricardo; Arango, Camila; Vercher-Martínez, Ana; Tarancón, J. E.

doi:10.1016/j.engfracmech.2017.08.026

Cited by 31 publications

(18 citation statements)

References 42 publications

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“…The stiffness for the matrix was measured under wet conditions. Symbols used in the table: ~ approximate value interpreted from figures; K G calculated from a reported stress intensity factor K , where G = K 2 / E , assuming E = 20 GPa (Koester et al 2008); T transverse osteons (crack parallel to osteons); L longitudinal osteons (crack perpendicular to osteons) a Faingold et al (2014); b Nyman et al (2006); c Rho et al (1999); d Rho et al (2002); e Mullins et al (2009); f Hengsberger et al (2002); g Skedros et al (2005); h Milovanovic et al (2018); i Burr et al (1988); j Montalbano and Feng (2011); k Chan et al (2009); l Gargac et al (2014); m Gustafsson et al (2018b); n Sun et al (2010); o Dong et al (2005); p Bigley et al (2006); q Norman et al (1995); r Zimmermann et al (2009); s Koester et al (2008); t Nalla et al (2005); u Mullins et al (2009); v Abdel-Wahab et al (2012); w Li et al (2013); x Vergani et al (2014); y Budyn and Hoc (2007); z Baptista et al (2016); aa Idkaidek and Jasiuk (2017); ab Wang et al (2017); ac Idkaidek and Jasiuk (2017); ad Budyn et al (2008); ae Demirtas et al (2016); af Rodriguez-Florez et al (2017); ag Giner et al (2017); ah Mischinski and Ural (2011); ai Nobakhti et al (2014)…”

Section: Methodsmentioning

confidence: 99%

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Gustafsson

Wallin

Khayyeri

et al. 2019

Biomech Model Mechanobiol

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Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone. Electronic supplementary material The online version of this article (10.1007/s10237-019-01142-4) contains supplementary material, which is available to authorized users.

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Section: Methodsmentioning

confidence: 99%

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Gustafsson

Wallin

Khayyeri

et al. 2019

Biomech Model Mechanobiol

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“…The cement line constitutes the interface between secondary osteons and the interstitial matrix. This is a less mineralized zone which exhibits low toughness and stiffness properties, leading to propagation of cracks around secondary osteons [17][18][19][20][21]. The cement line has been analysed in the literature for being the constituent at the microscale that shows the highest risk of failure in cortical bone tissue (see for instance [20][21][22][23][24][25]).…”

Section: At Different Scales)mentioning

confidence: 99%

“…secondary osteons, interstitial matrix and cement lines. In the literature there is a wide dispersion regarding bone mechanical properties [21,25,53,54]. This scatter in the material properties can also affect to the numerical estimation of bone fracture load [55].…”

Section: Application To Simplified Geometries Of Cortical Bonementioning

confidence: 99%

“…Given the problem conditions of our study, the mechanical properties of cortical bone components (cement line, interstitial matrix and secondary osteons) used in our numerical models are shown in Table 1. [19] 100 [11] 860 [17] D ost = 100 -300 [11,61] Interstitial matrix 14610 1 55 [62] 238 [17] -Cement line 88 [18] 6 [21] 163 [21] E cem = 5 [11] Haversian canal ---D hav = 20 -90 [63] In what follows, several numerical models (simplified and realistic) are solved.…”

Section: Application To Simplified Geometries Of Cortical Bonementioning

confidence: 99%

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A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach

Marco

Belda

Miguélez

et al. 2018

Finite Elements in Analysis and Design

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Cortical bone can be considered as a heterogeneous composite at microscopic scale, composed of osteons that act as reinforcement fibres embedded in interstitial matrix. Cement lines constitute the interface between osteons and matrix, and they often behave as the weakest links along which microcracks tend to propagate. However, current simulations of crack growth using XFEM combined with usual orientation criteria as implemented in commercial codes do not capture this behaviour: they predict crack paths that do not follow the cement lines surrounding osteons. The reason is that the orientation criterion used in the implementation of XFEM does not take into account the heterogeneity of the material, leading to simulations that differ from experimental results. In this work, a crack orientation criterion for heterogeneous materials based on interface damage prediction in composites is proposed and a phantom node approach has been implemented to model crack propagation. The method has been validated by means of linear elastic fracture mechanics (LEFM) problems obtaining accurate results. The procedure is applied to different problems including several osteons with simplified 2 geometry and an experimental test reported in the literature leading to satisfactory predictions of crack paths.

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“…• redução da rigidez da estrutura através da exclusão de elementos (em inglês, element deletion), visando reproduzir a propagação de fissuras (Donaldson et al, 2014;Giner et al, 2017);…”

Section: Introductionunclassified

Modelagem do processo de fissuração em osso cortical através da técnica de fragmentação de malha de elementos finitos.

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In this work, the crack initiation and propagation process in the microstructure of the cortical bone is simulated using the finite element method combined with a mesh fragmentation technique. Thus, triangular finite elements with high aspect ratio (elements with the base much greater than the height) are inserted in pairs between the interfaces of regular triangular elements, after the fragmentation process to describe the possible crack path trajectories. The microstructure of the cortical bone is modeled as a 4-phased composite material: interstitial matrix, cement line, osteon and Haversian canal. The material non-linearity is represented by the behavior of the high aspect ratio elements via a combined damage model with adequate mechanical properties assigned to each phase of the material. The methodology is employed in the numerical simulations of 6 conceptual representations of the microarchitecture of the cortical bone and 1 model based on the geometry extracted from a digital picture. The mechanical behavior is assessed in tension and bending tests while considering geometries with one or multiple osteons. The results demonstrated that the proposed technique based on the mesh fragmentation process is suitable to represent the crack initiation and propagation process in the cortical bone, with results in good agreement with those available in the literature, including the mechanical influence of the cement line in the cracking process.

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Calculation of the critical energy release rateGcof the cement line in cortical bone combining experimental tests and finite element models

Cited by 31 publications

References 42 publications

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach

Modelagem do processo de fissuração em osso cortical através da técnica de fragmentação de malha de elementos finitos.

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