In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Schwiedrzik, Jakob; Raghavan, R.; Bürki, Alexander; Lenader, Victor; Wolfram, Uwe; Michler, Johann; Zysset, Philippe

doi:10.1038/nmat3959

Cited by 160 publications

(211 citation statements)

References 55 publications

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“…The mineral external to the fibril can be either tightly bound to the surface of the MF 5 , which gives rise to a coated mineralized fibril, here referred to as CMF, or be a part of the extrafibrillar matrix, which we refer to as "EFM". The CMFs have been experimentally observed in bone, bridging cracks in 6 and on failure surfaces 7 , which suggests that it is important and relevant to calculate the stress concentration due to CMFs, . Figure S2.…”

Section: Stress Concentration From Fibersmentioning

confidence: 94%

The nanocomposite nature of bone drives its strength and damage resistance

2016

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Crystallization of ACP with timeTo probe the stability of the observed ACP in disordered phase with respect to the adjacent HA nanocrystals, we performed TEM analysis of the same region after a 30-day time lapse. During the 30 days, the TEM sample was stored at room temperature in a N2 environment. Figure S1a shows the initial arrangement of ACP (left) and HA nanocrystals (right), as well as the diffraction pattern inset showing the crystallinity of the HA. Figure S1b shows the same region after the 30 day incubation period; the HA nanocrystals on the right appear to have grown, confirmed by the increased (112), (211), (300) intensities in the diffraction pattern inset; we also observe the emergence of (002) reflections after one month, which further proves the formation of crystals. These results demonstrate suggest that biogenic ACP is a precursor for crystalline cHA formation in bone in the observed conditions, as similarly observed by Mahamid et al 1 . Figure S1. Time lapse micrographs of amorphous and nanocrystalline regions. Deprotonated mineral structure in disordered phase taken before (a) and after (b) a 30 day incubation at room temperature in a nitrogen environment. The electron diffraction pattern after the incubation (b, inset) shows an increase in crystallinity as evidenced by more intense HA reflections and the emergence of the (002) spots when compared to the initial diffraction pattern (a, inset). Size Dependent Model ConstructionWe propose that the yield strength, , decreases as the probability of having a flaw (i.e. a pore) on the pillar surface increases; that is, surface flaws serve as probabilistic stress concentrators, which initiate failure during compression. This is manifested most prevalently in the larger pillars, with diameters > 500nm. At these nano and micro length scales, it is reasonable to consider bone as a fiber-

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Section: Stress Concentration From Fibersmentioning

confidence: 94%

The nanocomposite nature of bone drives its strength and damage resistance

2016

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“…Experimental validation of the mechanical properties of bone at the nanoscale is also very challenging. Relevant experimental studies include atomic force microscopy measurements combined with electron microscopy imaging (SEM and TEM) (e.g., [58][59][60]) and tests on micropillars of bone at a µm scale [61][62][63]. Theoretical models can give valuable insights on bone's response at the nanoscale and the structure-property relations of bone in general.…”

Section: Modeling Of Bone At Nanoscale Various Geometric Modelsmentioning

confidence: 99%

The Ultrastructure of Bone and Its Relevance to Mechanical Properties

2017

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Bone is a biologically generated composite material comprised of two major structural components: crystals of apatite and collagen fibrils. Computational analysis of the mechanical properties of bone must make assumptions about the geometric and topological relationships between these components. Recent transmission electron microscope (TEM) studies of samples of bone prepared using ion milling methods have revealed important previously unrecognized features in the ultrastructure of bone. These studies show that most of the mineral in bone lies outside the fibrils and is organized into elongated plates 5 nanometers (nm) thick, ∼80 nm wide and hundreds of nm long. These so-called mineral lamellae (MLs) are mosaics of single 5 nm-thick, 20-50 nm wide crystals bonded at their edges. MLs occur either stacked around the 50 nm-diameter collagen fibrils, or in parallel stacks of 5 or more MLs situated between fibrils. About 20% of mineral is in gap zones within the fibrils. MLs are apparently glued together into mechanically coherent stacks which break across the stack rather than delaminating. ML stacks should behave as cohesive units during bone deformation. Finite element computations of mechanical properties of bone show that the model including such features generates greater stiffness and strength than are obtained using conventional models in which most of the mineral, in the form of isolated crystals, is situated inside collagen fibrils.

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“…While it has been widely agreed upon that bone shows a distinct tension-compression asymmetry in its yield properties, several different yield surfaces have been used in the past to model trabecular bone tissue such as principal-strain-based [25,26], cast iron [17,27], eccentric von Mises [28,29], or Drucker-Lode plasticity [30]. The use of plasticity models to determine apparent yield properties of trabecular bone from CT datasets is in line with the finding of elastoplastic deformation of bone tissue on the lamellar level up to moderate strains of 10-20%, which has been recently found in micropillar compression tests [31]. Based on micromechanical considerations and indentation measurements, it has been proposed that bone is a cohesive-frictional material [32] and may best be described on the microscale by a Drucker-Prager or Mohr-Coulomb yield criterion [32,33].…”

Section: Introductionmentioning

confidence: 64%

Experimental validation of a nonlinear μFE model based on cohesive‐frictional plasticity for trabecular bone

Schwiedrzik

Groß

Bina

et al. 2015

Numer Methods Biomed Eng

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Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

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In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Cited by 160 publications

References 55 publications

The nanocomposite nature of bone drives its strength and damage resistance

The nanocomposite nature of bone drives its strength and damage resistance

The Ultrastructure of Bone and Its Relevance to Mechanical Properties

Experimental validation of a nonlinear μFE model based on cohesive‐frictional plasticity for trabecular bone

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