Influences of spherical tip radius, contact depth, and contact area on nanoindentation properties of bone

Early Degenerative Changes in a Spontaneous Osteoarthritis Model Assessed by Nanoindentation

Understanding early mechanical changes in articular cartilage (AC) and subchondral bone (SB) is crucial for improved treatment of osteoarthritis (OA). The aim of this study was to develop a method for nanoindentation of fresh, unfixed osteochondral tissue to assess the early changes in the mechanical properties of AC and SB. Nanoindentation was performed throughout the depth of AC and SB in the proximal tibia of Dunkin Hartley guinea pigs at 2 months, 3 months, and 2 years of age. The contralateral tibias were either histologically graded for OA or analyzed using immunohistochemistry. The results showed an increase in the reduced modulus (Er) in the deep zone of AC during early-stage OA (6.0 ± 1.75 MPa) compared to values at 2 months (4.04 ± 1.25 MPa) (*** p < 0.001). In severe OA (2-year) specimens, there was a significant reduction in Er throughout the superficial and middle AC zones, which correlated to increased ADAMTS 4 and 5 staining, and proteoglycan loss in these regions. In the subchondral bone, a 35.0% reduction in stiffness was observed between 2-month and 3-month specimens (*** p < 0.001). The severe OA age group had significantly increased SB stiffness of 36.2% and 109.6% compared to 2-month and 3-month-old specimens respectively (*** p < 0.001). In conclusion, this study provides useful information about the changes in the mechanical properties of both AC and SB during both early- and late-stage OA and indicates that an initial reduction in stiffness of the SB and an increase in stiffness in the deep zone of AC may precede early-stage cartilage degeneration.

Exploring the Mechanical Properties and Performance of Type-I Collagen at Various Length Scales: A Progress Report

Collagen is the basic protein of animal tissues and has a complex hierarchical structure. It plays a crucial role in maintaining the mechanical and structural stability of biological tissues. Over the years, it has become a material of interest in the biomedical industries thanks to its excellent biocompatibility and biodegradability and low antigenicity. Despite its significance, the mechanical properties and performance of pure collagen have been never reviewed. In this work, the emphasis is on the mechanics of collagen at different hierarchical levels and its long-term mechanical performance. In addition, the effect of hydration, important for various applications, was considered throughout the study because of its dramatic influence on the mechanics of collagen. Furthermore, the discrepancies in reports of the mechanical properties of collagenous tissues (basically composed of 20-30% collagen fibres) and those of pure collagen are discussed.

Effect of Zirconia Nanofibers Structure Evolution on the Hardness and Young's Modulus of Their Mats

Zirconia nanofiber mats containing filaments with the average diameter of less than 100 nm were fabricated. It is found that the hardness and Young’s modulus of the mats are sensitive to the microstructure, phase composition and average diameter of the zirconia nanofibers. The hardness and Young’s modulus of the prepared zirconia nanofiber mats vary from 0.86 to 1.67 MPa and from 133 to 362 MPa, respectively, wherein an increase in hardness is accompanied by the rise in Young’s modulus.

A comparative assessment of consolidation materials applied to burned bone

Fire-altered or fragmentary bone presents a challenge to forensic anthropologists and bioarchaeologists due to its characteristic friability. A potential solution to this problem is the use of consolidant materials on fragile osteological material, including burned remains. Although anthropologists and odontologists employ a variety of consolidant materials, there is no consensus regarding which material is most appropriate. Four easily obtained and commonly used consolidants, Acryloid™ B-72, Acrysol™ WS-24, Rhoplex™ B-60A, and Butvar® B-98, were compared to assess ease of material application and ability to stabilize burned bone. Each consolidant was applied to a subgroup of the study population at a 10% concentration. Total dry time per specimen, ease of solution preparation and application, and any alteration to the bone's appearance were recorded to assess the practical use of each material in field recovery settings. Nanoindentation, drop weight impact, and forced vibration tests were then performed to assess degree of stabilization. These tests were chosen to mimic possible real-world scenarios where burned bone may undergo damage during and after recovery, including repeated handling and transportation from the fire scene to the lab. Based on both qualitative and quantitative data collected, Acryloid™ B-72 is the most suitable consolidant tested to stabilize burned or fragmentary bone during recovery efforts. If the dry time for Rhoplex™ B-60A could be reduced by using a different solvent, such as acetone, Rhoplex™ B-60A would also be appropriate. Highly calcined areas, and targeted structures that could be utilized for positive identification, including teeth and the frontal sinus, should preferentially be consolidated with Acryloid™ B-72 in the field prior to recovery.

Spatial localization of mechanical excitation affects spatial resolution, contrast, and contrast-to-noise ratio in acoustic radiation force optical coherence elastography

The notion that a spatially confined mechanical excitation would produce an elastogram with high spatial resolution has motivated the development of various elastography techniques with localized mechanical excitation. However, a quantitative investigation of the effects of spatial localization of mechanical excitation on the spatial resolution of elastograms is still lacking in optical coherence elastography (OCE). Here, we experimentally investigated the effect of spatial localization of acoustic radiation force (ARF) excitation on spatial resolution, contrast, and contrast-to-noise ratio (CNR) of dynamic uniaxial strain elastograms in dynamic ARF-OCE, based on a framework for analyzing the factors that influence the quality of the elastogram at different stages of the elastography workflow. Our results show that localized ARF excitation with a smaller acoustic focal spot size produced a strain elastogram with superior spatial resolution, contrast, and CNR. Our results also suggest that the spatial extent spanned by the displacement response in the sample may connect between the spatial localization of the mechanical excitation and the resulting elastogram quality. The elastography framework and experimental approach presented here may provide a basis for the quantitative analysis of elastogram quality in OCE that can be adapted and applied to different OCE systems and applications.

Assessing bone quality through mechanical properties in postmenopausal trabecular bone

BACKGROUND

The inner structure of trabecular bone is a result of structural optimization provided by remodeling processes. Changes in hormonal status related to menopause cause bone tissue loss and micro-architectural deterioration with a consequent susceptibility to fracture. Accumulation of micro-damage in bone, as a function of the rate of production and rate of repair, underlies the development of stress fractures, increasing fragility associated to age and osteoporosis, especially in transmenopausal women.

PATIENTS AND METHODS

Quasi-static and nano-dynamic mechanical characterization were undertaken in trabecular bone from femoral neck biopsies of postmenopausal women. AFM (Atomic Force Microscopy) complementary studies were performed to determine nano-roughness (SRa) and the fibrils width of collagen. Nanoindentations were used to quantify transmenopausal changes in intrinsic mechanical properties of trabecular bone: hardness (Hi), modulus of Young (Ei), complex modulus (E*), tan delta (δ), storage modulus (E') and loss modulus (E").

RESULTS

As result of the quasi-static measurements, 0.149 (0.036) GPa and 2.95 (0.73) GPa of Hi and Ei were obtained, respectively. As result of the nano-dynamic measurements, 17.94 (3.15), 0.62 (0.10), 13.79 (3.21 and 6.39 (1.28) GPa of E*, tan (δ), E' and E" were achieved, respectively. 101.07 SRa and 831.28 nm of fibrils width were additionally obtained.

CONCLUSIONS

This study poses a first approach to the measurement of bone quality in postmenopausal trabecular bone by combining quasi-static, nano-DMA analysis and tribology of dentin surface through AFM characterization.

Multiscale characterization of cortical bone composition, microstructure, and nanomechanical properties in experimentally induced osteoporosis

Cortical bone plays a vital role in determining overall bone strength. We investigate the structural, compositional, and nanomechanical properties of cortical bone following ovariectomy (OVX) of 12-week-old Sprague Dawley rats, since this animal model is frequently employed to evaluate the performance of implantable biomaterials in compromised bone healing conditions. Morphological parameters and material properties of bone in the geometrical center of the femoral cortex were investigated four and eight weeks post-OVX and in unoperated controls (Ctrl), using X-ray micro-computed tomography, backscattered electron scanning electron microscopy, Raman spectroscopy, and nanoindentation. The OVX animals showed increase in body weight, diminished bone mineral density, increased intracortical porosity, but increased bone mass through periosteal apposition (e.g., increases in periosteal perimeter, cortical cross-sectional thickness, and cross-sectional area). However, osteocyte densities, osteocyte lacunar dimensions, and the nanomechanical behavior on the single mineralized collagen fibril level remained unaffected. Our correlative multiscale investigation provides structural, chemical, and nanomechanical evidence substantiating earlier reports suggesting that rats ovariectomized at 12 weeks undergo simultaneous bone loss and growth, resulting in the effects of OVX being less obvious. Periosteal apposition contradicts the conventional view of bone loss in osteoporosis but appears advantageous for the greater functional demand imposed on the skeleton by increased body weight and fragility induced by increased intracortical porosity. Through a variety of morphological changes, it is likely that 12-week-old rats are able to adapt to OVX-related microstructural and compositional alterations. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 106A: 997-1007, 2018.

The inferomedial femoral neck is compromised by age but not disease: Fracture toughness and the multifactorial mechanisms comprising reference point microindentation

The influence of ageing on the fracture mechanics of cortical bone tissue is well documented, though little is known about if and how related material properties are further affected in two of the most prominent musculoskeletal diseases, osteoporosis and osteoarthritis (OA). The femoral neck, in close proximity to the most pertinent osteoporotic fracture site and near the hip joint affected by osteoarthritis, is a site of particular interest for investigation. We have recently shown that Reference Point micro-Indentation (RPI) detects differences between cortical bone from the femoral neck of healthy, osteoporotic fractured and osteoarthritic hip replacement patients. RPI is a new technique with potential for in vivo bone quality assessment. However, interpretation of RPI results is limited because the specific changes in bone properties with pathology are not well understood and, further, because it is not conclusive what properties are being assessed by RPI. Here, we investigate whether the differences previously detected between healthy and diseased cortical bone from the femoral neck might reflect changes in fracture toughness. Together with this, we investigate which additional properties are reflected in RPI measures. RPI (using the Biodent device) and fracture toughness tests were conducted on samples from the inferomedial neck of bone resected from donors with: OA (41 samples from 15 donors), osteoporosis (48 samples from 14 donors) and non age-matched cadaveric controls (37 samples from 10 donoros) with no history of bone disease. Further, a subset of indented samples were imaged using micro-computed tomography (3 osteoporotic and 4 control samples each from different donors) as well as fluorescence microscopy in combination with serial sectioning after basic fuchsin staining (7 osteoporotic and 5 control samples from 5 osteoporotic and 5 control donors). In this study, the bulk indentation and fracture resistance properties of the inferomedial femoral neck in osteoporotic fracture, severe OA and control bone were comparable (p > 0.05 for fracture properties and <10% difference for indentation) but fracture toughness reduced with advancing age (7.0% per decade, r = -0.36, p = 0.029). Further, RPI properties (in particular, the indentation distance increase, IDI) showed partial correlation with fracture toughness (r = -0.40, p = 0.023) or derived elastic modulus (r = -0.40, p = 0.023). Multimodal indent imaging revealed evidence of toughening mechanisms (i.e. crack deflection, bridging and microcracking), elastoplastic response (in terms of the non-conical imprint shape and presence of pile-up) and correlation of RPI with damage extent (up to r = 0.79, p = 0.034) and indent size (up to r = 0.82, p < 0.001). Therefore, crack resistance, deformation resistance and, additionally, micro-structure (porosity: r = 0.93, p = 0.002 as well as pore proximity: r = -0.55, p = 0.027 for correlation with IDI) are all contributory to RPI. Consequently, it becomes clear that RPI measures represent a multitude of properties, various aspects of bone quality, but are not necessarily strongly correlated to a single mechanical property. In addition, osteoporosis or osteoarthritis do not seem to further influence fracture toughness of the inferomedial femoral neck beyond natural ageing. Since bone is highly heterogeneous, whether this finding can be extended to the whole femoral neck or whether it also holds true for other femoral neck quadrants or other material properties remains to be shown.

Multi-Scale Mechanical Behavior of the Li3PS4 Solid-Phase Electrolyte

The need for smaller, lighter, and longer lasting rechargeable batteries is projected to increase rapidly in the coming years because of high demand for portable electronics and electric vehicles. While traditional Li-ion batteries use liquid-phase electrolytes, these suffer from safety risks and low energy density. Solid-phase electrolytes can avoid these issues by enabling a Li metal anode, but tend to fail during cycling due to Li metal dendrite growth between the electrodes. Because Li dendrite nucleation and growth can be viewed in terms of the mechanical behavior of the battery components, it is critical to understand the mechanical response of candidate electrolyte materials. In this work, we use nanoindentation and bulk acoustic techniques to characterize the mechanical properties of β-Li₃PS₄, a promising Li-ion conducting ceramic. We find that the bulk and shear moduli of an 80% dense bulk LPS sample are 10-12 GPa and 5-6 GPa, respectively. Although this value of shear modulus may be too low to prevent Li dendrite propagation, it is likely that there are many other mechanical properties that must be taken into account to fully understand Li dendrite nucleation and growth. Ultimately, this work represents a first step in understanding the relationship between Li₃PS₄ separator manufacture and its mechanical properties.

Moderate chronic kidney disease impairs bone quality in C57Bl/6J mice

Chronic kidney disease (CKD) increases bone fracture risk. While the causes of bone fragility in CKD are not clear, the disrupted mineral homeostasis inherent to CKD may cause material quality changes to bone tissue. In this study, 11-week-old male C57Bl/6J mice underwent either 5/6th nephrectomy (5/6 Nx) or sham surgeries. Mice were fed a normal chow diet and euthanized 11weeks post-surgery. Moderate CKD with high bone turnover was established in the 5/6 Nx group as determined through serum chemistry and bone gene expression assays. We compared nanoindentation modulus and mineral volume fraction (assessed through quantitative backscattered scanning electron microscopy) at matched sites in arrays placed on the cortical bone of the tibia mid-diaphysis. Trabecular and cortical bone microarchitecture and whole bone strength were also evaluated. We found that moderate CKD minimally affected bone microarchitecture and did not influence whole bone strength. Meanwhile, bone material quality decreased with CKD; a pattern of altered tissue maturation was observed with 5/6 Nx whereby the newest 60μm of bone tissue adjacent to the periosteal surface had lower indentation modulus and mineral volume fraction than more interior, older bone. The variance of modulus and mineral volume fraction was also altered following 5/6 Nx, implying that tissue-scale heterogeneity may be negatively affected by CKD. The observed lower bone material quality may play a role in the decreased fracture resistance that is clinically associated with human CKD.

Application of Elastography for the Noninvasive Assessment of Biomechanics in Engineered Biomaterials and Tissues

The elastic properties of engineered biomaterials and tissues impact their post-implantation repair potential and structural integrity, and are critical to help regulate cell fate and gene expression. The measurement of properties (e.g., stiffness or shear modulus) can be attained using elastography, which exploits noninvasive imaging modalities to provide functional information of a material indicative of the regeneration state. In this review, we outline the current leading elastography methodologies available to characterize the properties of biomaterials and tissues suitable for repair and mechanobiology research. We describe methods utilizing magnetic resonance, ultrasound, and optical coherent elastography, highlighting their potential for longitudinal monitoring of implanted materials in vivo, in addition to spatiotemporal limits of each method for probing changes in cell-laden constructs. Micro-elastography methods now allow acquisitions at length scales approaching 5-100 μm in two and three dimensions. Many of the methods introduced in this review are therefore capable of longitudinal monitoring in biomaterials and tissues approaching the cellular scale. However, critical factors such as anisotropy, heterogeneity and viscoelasity-inherent in many soft tissues-are often not fully described and therefore require further advancements and future developments.

NANOINDENTATION AND ASH CONTENT STUDY OF AGE DEPENDENT CHANGES IN PORCINE CORTICAL BONE

Composition-structure-property relations of bone provide fundamental understanding of bone quality. The objective of this paper was to investigate age dependent changes in the composition, structure and mechanical properties of porcine femoral cortical bone at mid-diaphysis region from six age groups (1, 3.5, 6, 12, 30, 48 months). This study was motivated by the fact that limited data is available in the literature on young porcine cortical bone. Nanoindentation technique with Berkovich fluid cell tip was employed to measure the elastic modulus and hardness. Individual lamellae were indented in the longitudinal direction of bone in different microstructural components (osteonal, interstitial and plexiform bone). A grid of indentations was also made on one bone sample to obtain spatial variations in the elastic modulus and hardness. Ash and water content tests were performed to measure water, organic and mineral contents of bone as a function of age. Finally, high resolution micro-computed tomography was used to measure porosity and visualize three-dimensional void structures. We found that the elastic modulus and hardness of bone increased with age but at different rates in each microstructural component. The mineral content increased correspondingly with age while the porosity decreased. The obtained structure, composition, and mechanical properties data give new insights on the age related changes in young cortical bone and can serve as inputs for and validation of multiscale models of bone.

Finite-element modeling and analysis in nanomedicine and dentistry

This article aims to provide a brief background to the current applications of finite-element analysis (FEA) in nanomedicine and dentistry. FEA was introduced in orthopedic biomechanics in the 1970s in order to assess the stresses and deformation in human bones during functional loadings and in the design and analysis of implants. Since then, it has been applied with great frequency in orthopedics and dentistry in order to analyze issues such as implant design, bone remodeling and fracture healing, the mechanical properties of biomedical coatings on implants and the interactions at the bone–implant interface. More recently, FEA has been used in nanomedicine to study the mechanics of a single cell and to gain fundamental insights into how the particulate nature of blood influences nanoparticle delivery.

Deleterious effects of osteoarthritis on the structure and function of the meniscal enthesis

OBJECTIVE

The ability of menisci to prevent osteoarthritis (OA) is dependent on the integrity of the complex meniscal entheses, the attachments of the menisci to the underlying subchondral bone (SB). The goal of this study was to determine mechanical and structural changes in meniscal entheses after the onset of OA.

DESIGN

Healthy and osteoarthritic meniscal entheses were evaluated for changes in histomorphological characteristics, mineralization, and mechanical properties. Glycosaminoglycans (GAG) and calcium in the insertion were evaluated with histological staining techniques. The extent of calcium deposition was assessed and tidemark (TM) integrity was quantified. Changes in the mineralized zone of the insertion were examined using micro-computed tomography (μCT) to determine bone mineral density, cortical zone thickness, and mineralization gradient. Mechanical properties of the entheses were measured using nano-indentation techniques to obtain material properties based on viscoelastic analysis.

RESULTS

GAG thickness in the calcified fibrocartilage (CFC) zone and calcium content were significantly greater in osteoarthritic anterior meniscal entheses. TM integrity was significantly decreased in OA tissue, particularly in the medial anterior (MA) enthesis. The mineralized zone of osteoarthritic meniscal entheses was significantly thicker than in healthy entheses and showed decreased bone mineral density. Fitting of mineralization data to a sigmoidal Gompertz function revealed a lower rate of increase in mineralization in osteoarthritic tissue. Analysis of viscoelastic mechanical properties revealed increased compliance in osteoarthritic tissue.

CONCLUSIONS

These data suggest that significant changes occur at meniscal enthesis sites with the onset of OA. Mechanical and structural changes in meniscal entheses may contribute to meniscal extrusion, which has been shown to increase the progression of OA.

Adipose-derived stem cells and rabbit bone regeneration: histomorphometric, immunohistochemical and mechanical characterization

BACKGROUND

In the last few years, several attempts have been made to treat large bone loss, including the use of tissue engineering with osteoinductive scaffolds and cells. This study highlights the role of mesenchymal stem cells from adipose tissue (ASCs; adipose-derived stem cells) in a rabbit bone regeneration model.

METHODS

We compared the neoformed bone tissues achieved by treating critical tibial defects with either hydroxyapatite alone (HA, group I) or hydroxyapatite-autologous ASC constructs (ASCs-HA, group II), investigating their histomorphometric, immunohistochemical and biomechanical properties.

RESULTS

After eight weeks of follow-up, we observed advanced maturation and a spatial distribution of new bone that was more homogeneous in the inner parts of the pores in group II, not just along the walls (as seen in group I). The new tissue expressed osteogenic markers, and biomechanical tests suggested that the newly formed bone in group II had a higher mineral content than that in group I. Although variability in differentiation was observed among the different cell populations in vitro, no differences in bone healing were observed in vivo; the variability seen in vitro was probably due to local microenvironment effects.

CONCLUSIONS

Tibial defects treated with rabbit ASCs-HA showed an improved healing process when compared to the process that occurred when only the scaffold was used. We suggest that implanted ASCs ameliorate the bone reparative process either directly or by recruiting resident progenitor cells.

Microcrack density and nanomechanical properties in the subchondral region of the immature piglet femoral head following ischemic osteonecrosis

Development of a subchondral fracture is one of the earliest signs of structural failure of the immature femoral head following ischemic osteonecrosis, and this eventually leads to a flattening deformity of the femoral head. The mechanical and mineralization changes in the femoral head preceding subchondral fracture have not been elucidated. We hypothesized that ischemic osteonecrosis leads to early material and mechanical alterations in the bone of the subchondral region. The purpose of this investigation was to assess the bone of the subchondral region for changes in the histology of bone cells, microcrack density, mineral content, and nanoindentation properties at an early stage of ischemic osteonecrosis in a piglet model. This large animal model has been shown to develop a subchondral fracture and femoral head deformity resembling juvenile femoral head osteonecrosis. The unoperated, left femoral head of each piglet (n=8) was used as a normal control, while the right side had a surgical ischemia induced by disrupting the femoral neck vessels with a ligature. Hematoxylin and eosin (H&E) staining and TUNEL assay were performed on femoral heads from 3 piglets. Quantitative backscattered electron imaging, nanoindentation, and microcrack assessments were performed on the subchondral region of both control and ischemic femoral heads from 5 piglets. H&E staining and TUNEL assay showed extensive cell death and an absence of osteoblasts in the ischemic side compared to the normal control. Microcrack density in the ischemic side (3.2±0.79 cracks/mm(2)) was significantly higher compared to the normal side (0.27±0.27 cracks/mm(2)) in the subchondral region (p<0.05). The weighted mean of the weight percent distribution of calcium (CaMean) also was significantly higher in the ischemic subchondral region (p<0.05). Furthermore, the nanoindentation modulus within localized areas of subchondral bone was significantly increased in the ischemic side (16.8±2.7GPa) compared to the normal control (13.3±3.2GPa) (p<0.05). Taken together, these results support the hypothesis that the nanoindentation modulus of the subchondral trabecular bone is increased in the early stage of ischemic osteonecrosis of the immature femoral head and makes it more susceptible to microcrack formation. We postulate that continued loading of the hip joint when there is a lack of bone cells to repair the microcracks due to ischemic osteonecrosis leads to microcrack accumulation and subsequent subchondral fracture.

Assessment of lamellar level properties in mouse bone utilizing a novel spherical nanoindentation data analysis method

In this work, we demonstrate the viability of using our recently developed data analysis procedures for spherical nanoindentation in conjunction with Raman spectroscopy for studying lamellar-level correlations between the local composition and local mechanical properties in mouse bone. Our methodologies allow us to convert the raw load-displacement datasets to much more meaningful indentation stress-strain curves that accurately capture the loading and unloading elastic moduli, the indentation yield points, as well as the post-yield characteristics in the tested samples. Using samples of two different inbred mouse strains, A/J and C57BL/6J (B6), we successfully demonstrate the correlations between the mechanical information obtained from spherical nanoindentation measurements to the local composition measured using Raman spectroscopy. In particular, we observe that a higher mineral-to-matrix ratio correlated well with a higher local modulus and yield strength in all samples. Thus, new bone regions exhibited lower moduli and yield strengths compared to more mature bone. The B6 mice were also found to exhibit lower modulus and yield strength values compared to the more mineralized A/J strain.

Intrinsic material properties of trabecular bone by nanoindentation testing of biopsies taken from healthy women before and after menopause

Postmenopausal osteoporosis in women is characterized by an increase in bone fragility and risk of fracture. In addition to transmenopausal decline in three-dimensional trabecular bone architecture, changes in intrinsic material properties (local stiffness, damping, and hardness) may contribute to increased bone fragility. In this study, nanoindentation was used to quantify transmenopausal changes in the intrinsic properties of trabecular bone. Paired transilial biopsy specimens were used from a previously reported study in which bone biopsies were obtained from women prior to menopause (premenopausal, age 49.0 ± 1.9) and at 12 months past the last menstrual period (postmenopausal, age 54.6 ± 2.2). Elastic and viscoelastic material properties of the trabecular bone were measured using quasi-static and dynamic nanoindentation techniques, respectively. Paired Student's t tests (n = 15) were performed to assess the significance of the measured intrinsic properties. Trabecular bone microarchitecture is compromised in postmenopausal women, and although this loss is associated with a trend toward reduction in some intrinsic properties (storage modulus), we found no statistically significant changes in bone intrinsic properties between healthy pre- and postmenopausal biopsies in the quasi-static results and frequency-averaged dynamic results.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elastoplastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two-dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 μm and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E = 13.56 GPa and Poisson's ratio of 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5 mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 μm with a von Mises model, and from 0.09 to 0.02 μm with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.