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.

Relating in situ gas measurements to the surface outgassing properties of cometary nuclei

The sensitivity of the gas flow field to changes in different initial conditions has been studied for the case of a highly simplified cometary nucleus model. The nucleus model simulated a homogeneously outgassing sphere with a more active ring around an axis of symmetry. The varied initial conditions were the number density of the homogeneous region, the surface temperature, and the composition of the flow (varying amounts of H2O and CO2) from the active ring. The sensitivity analysis was performed using the Polynomial Chaos Expansion (PCE) method. Direct Simulation Monte Carlo (DSMC) was used for the flow, thereby allowing strong deviations from local thermal equilibrium. The PCE approach can be used to produce a sensitivity analysis with only four runs per modified input parameter and allows one to study and quantify non-linear responses of measurable parameters to linear changes in the input over a wide range. Hence the PCE allows one to obtain a functional relationship between the flow field properties at every point in the inner coma and the input conditions. It is for example shown that the velocity and the temperature of the background gas are not simply linear functions of the initial number density at the source. As probably expected, the main influence on the resulting flow field parameter is the corresponding initial parameter (i.e. the initial number density determines the background number density, the temperature of the surface determines the flow field temperature, etc.). However, the velocity of the flow field is also influenced by the surface temperature while the number density is not sensitive to the surface temperature at all in our model set-up. Another example is the change in the composition of the flow over the active area. Such changes can be seen in the velocity but again not in the number density. Although this study uses only a simple test case, we suggest that the approach, when applied to a real case in 3D, should assist in identifying the sensitivity of gas parameters measured in situ by, for example, the Rosetta spacecraft to the surface boundary conditions and vice versa.

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

Correlation between alveolar ventilation and electrical properties of lung parenchyma.

One key problem in modern medical imaging is linking measured data and actual physiological quantities. In this article we derive such a link between the electrical bioimpedance of lung parenchyma, which can be measured by electrical impedance tomography (EIT), and the magnitude of regional ventilation, a key to understanding lung mechanics and developing novel protective ventilation strategies. Two rat-derived three-dimensional alveolar microstructures obtained from synchrotron-based x-ray tomography are each exposed to a constant potential difference for different states of ventilation in a finite element simulation. While the alveolar wall volume remains constant during stretch, the enclosed air volume varies, similar to the lung volume during ventilation. The enclosed air, serving as insulator in the alveolar ensemble, determines the resulting current and accordingly local tissue bioimpedance. From this we can derive a relationship between lung tissue bioimpedance and regional alveolar ventilation. The derived relationship shows a linear dependence between air content and tissue impedance and matches clinical data determined from a ventilated patient at the bedside.

Spectrophotometric properties of the nucleus of comet 67P/Churyumov-Gerasimenko from the OSIRIS instrument onboard the ROSETTA spacecraft

Context. The Rosetta mission of the European Space Agency has been orbiting the comet 67P/Churyumov-Gerasimenko (67P) since August 2014 and is now in its escort phase. A large complement of scientific experiments designed to complete the most detailed study of a comet ever attempted are onboard Rosetta. Aims. We present results for the photometric and spectrophotometric properties of the nucleus of 67P derived from the OSIRIS imaging system, which consists of a Wide Angle Camera (WAC) and a Narrow Angle Camera (NAC). The observations presented here were performed during July and the beginning of August 2014, during the approach phase, when OSIRIS was mapping the surface of the comet with several filters at different phase angles (1.3 degrees-54 degrees). The resolution reached up to 2.1 m/px. Methods. The OSIRIS images were processed with the OSIRIS standard pipeline, then converted into I/F. radiance factors and corrected for the illumination conditions at each pixel using the Lommel-Seeliger disk law. Color cubes of the surface were produced by stacking registered and illumination-corrected images. Furthermore, photometric analysis was performed both on disk-averaged photometry in several filters and on disk-resolved images acquired with the NAC orange filter, centered at 649 ran, using Hapke modeling. Results. The disk-averaged phase function of the nucleus of 67P shows a strong opposition surge with a G parameter value of -0.13 +/- 0.01 in the HG system formalism and an absolute magnitude H-v(1, 1, 0) = 15.74 +/- 0.02 mag. The integrated spectrophotometry in 20 filters covering the 250-1000 nm wavelength range shows a red spectral behavior, without clear absorption bands except for a potential absorption centered at similar to 290 rim that is possibly due to SO2 ice. The nucleus shows strong phase reddening, with disk-averaged spectral slopes increasing from 11%/( 100 nm) to 16%/(100 nm) in the 1.3 degrees-54 degrees phase angle range. The geometric albedo of the comet is 6.5 +/- 0.2% at 649 nm, with local variations of up to similar to 16% in the Hapi region. From the disk-resolved images we computed the spectral slope together with local spectrophotometry and identified three distinct groups of regions (blue, moderately red, and red). The Hapi region is the brightest, the bluest in term of spectral slope, and the most active surface on the comet. Local spectrophotometry shows an enhancement of the flux in the 700-750 nm that is associated with coma emissions.

Thermal and mechanical properties of the near-surface layers of comet 67P/Churyumov-Gerasimenko

Thermal and mechanical material properties determine comet evolution and even solar system formation because comets are considered remnant volatile-rich planetesimals. Using data from the Multipurpose Sensors for Surface and Sub-Surface Science (MUPUS) instrument package gathered at the Philae landing site Abydos on comet 67P/Churyumov-Gerasimenko, we found the diurnal temperature to vary between 90 and 130 K. The surface emissivity was 0.97, and the local thermal inertia was 85 +/- 35 J m(-2) K(-1)s(-1/2). The MUPUS thermal probe did not fully penetrate the near-surface layers, suggesting a local resistance of the ground to penetration of >4 megapascals, equivalent to >2 megapascal uniaxial compressive strength. A sintered near-surface microporous dust-ice layer with a porosity of 30 to 65% is consistent with the data.

Imaging properties of scanning equalization digital radiography: A simulation study

We have developed an empirically based simulation system to create images equivalent in SNR and SPR to those that would be acquired with various possible SEDR configurations. This system uses a collection of spot collimated full-field images (SCFFIs) of an anthropomorphic chest phantom, taken at high exposure levels and rescaled in noise and intensity, then digitally collimated and combined to produce the simulated SEDR images. This system allows for the study of design trade-offs between different equalization feedback schemes and scatter rejection geometries in addition to estimating the clinical benefits of SEDR over traditional imaging techniques. Data from this simulation system has demonstrated that SEDR techniques offer potential significant improvements over currently used digital radiography techniques for chest imaging. ^

Sea ice physics from the southern Weddell Sea

During the German Antarctic Expedition 1979/80, the sea ice conditions in the Weddell Sea were studied along the ice shelf between Cape Fiske (root of the Antarctlc Peninsula) and Atka Bay. Most intensively was the sea ice investigated in an area about 100 km northwest of Berkner Island, where a suitable site for the German station was found. In addition to the drift conditions, ice thickness as weIl as temperature and salinity of the ice were measured and the mechanical properties established. Several ice cores were taken back to Germany, where the compressive strength was measured in respect to strain rate, salinity, depth and temperature.

Physics, geochemistry and bulk sedimentology on cores from the Peru Basin

Empirical relationships between physical properties determined non-destructively by core logging devices and calibrated by carbonate and opal measurements determined on discrete samples allow extraction of carbonate and opal records from the non-destructive measurements in biogenic settings. Contents of detrital material can be calculated as a residual. For carbonate and opal the correlation coefficients (r) are 0.954 and ?0.916 for sediment density, ?0.816 and 0.845 for compressional-wave velocity, 0.908 and ?0.942 for acoustic impedance, and 0.886 and ?0.865 for sediment color (lightness). Carbonate contents increase in concert with increasing density and acoustic impedance, decreasing velocity and lighter sediment color. The opposite is true for opal. The advantages of deriving the sediment composition quantitatively from core logging are: (i) sampling resolution is increased significantly, (ii) non-destructive data can be gathered rapidly, and (iii) laboratory work on discrete samples can be reduced. Applied to paleoceanographic problems, this method offers the opportunity of precise stratigraphic correlations and of studying processes related to biogenic sedimentation in more detail. Density is most promising because it is most strongly affected by changes in composition.