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

Ageing societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the hierarchical organization of bone. Here, we investigate the mechanical response under monotonic and cyclic compression of both single osteonal lamellae and macroscopic samples containing numerous osteons. Micropillar compression tests in a scanning electron microscope, microindentation and macroscopic compression tests were performed on dry ovine bone to identify the elastic modulus, yield stress, plastic deformation, damage accumulation and failure mechanisms. We found that isolated lamellae exhibit a plastic behaviour, with higher yield stress and ductility but no damage. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behaviour of bone at the microscale to a quasi-brittle response driven by the growth of cracks along interfaces or in the vicinity of pores at the macroscale.

Augmentation of mechanical properties in osteoporotic vertebral bones--a biomechanical investigation of vertebroplasty efficacy with different bone cements

Recent clinical trials have reported favorable early results for transpedicular vertebral cement reinforcement of osteoporotic vertebral insufficiencies. There is, however, a lack of basic data on the application, safety and biomechanical efficacy of materials such as polymethyl-methacrylate (PMMA) and calciumphospate (CaP) cements. The present study analyzed 33 vertebral pairs from five human cadaver spines. Thirty-nine vertebrae were osteoporotic (bone mineral density < 0.75 g/cm2), 27 showed nearly normal values. The cranial vertebra of each pair was augmented with either PMMA (Palacos E-Flow) or experimental brushite cement (EBC), with the caudal vertebra as a control. PMMA and EBC were easy to inject, and vertebral fillings of 20-50% were achieved. The maximal possible filling was inversely correlated to the bone mineral density (BMD) values. Cement extrusion into the spinal canal was observed in 12% of cases. All specimens were subjected to axial compression tests in a displacement-controlled mode. From load-displacement curves, the stiffness, S, and the maximal force before failure, Fmax, were determined. Compared with the native control vertebrae, a statistically significant increase in vertebral stiffness and Fmax was observed by the augmentation. With PMMA the stiffness increased by 174% (P = 0.018) and Fmax by 195% (P = 0.001); the corresponding augmentation with EBC was 120% (P = 0.03) and 113% (P = 0.002). The lower the initial BMD, the more pronounced was the augmentation effect. Both PMMA and EBC augmentation reliably and significantly raised the stiffness and maximal tolerable force until failure in osteoporotic vertebral bodies. In non-porotic specimens, no significant increase was achieved.

Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towardsthe prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Properties of granular analogue model materials: A community wide survey

We report the material properties of 26 granular analogue materials used in 14 analogue modelling laboratories. We determined physical characteristics such as bulk density, grain size distribution, and grain shape, and performed ring shear tests to determine friction angles and cohesion, and uniaxial compression tests to evaluate the compaction behaviour. Mean grain size of the materials varied between c. 100 and 400 μm. Analysis of grain shape factors shows that the four different classes of granular materials (14 quartz sands, 5 dyed quartz sands, 4 heavy mineral sands and 3 size fractions of glass beads) can be broadly divided into two groups consisting of 12 angular and 14 rounded materials. Grain shape has an influence on friction angles, with most angular materials having higher internal friction angles (between c. 35° and 40°) than rounded materials, whereas well-rounded glass beads have the lowest internal friction angles (between c. 25° and 30°). We interpret this as an effect of intergranular sliding versus rolling. Most angular materials have also higher basal friction angles (tested for a specific foil) than more rounded materials, suggesting that angular grains scratch and wear the foil. Most materials have an internal cohesion in the order of 20–100 Pa except for well-rounded glass beads, which show a trend towards a quasi-cohesionless (C < 20 Pa) Coulomb-type material. The uniaxial confined compression tests reveal that rounded grains generally show less compaction than angular grains. We interpret this to be related to the initial packing density after sifting, which is higher for rounded grains than for angular grains. Ring-shear test data show that angular grains undergo a longer strain-hardening phase than more rounded materials. This might explain why analogue models consisting of angular grains accommodate deformation in a more distributed manner prior to strain localisation than models consisting of rounded grains.