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.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Impact of normal and shear stresses due to wheel slip on hydrological properties of an agricultural clay loam: Experimental and new computerized approach

The main purpose of this study was to evaluate the effect that mechanical stresses acting under the slipping driving wheels of agricultural equipment have on the soil’s pore system and water flow process (surface runoff generation during extreme event). The field experiment simulated low slip (1%) and high slip (27%) on a clay loam. The stress on the soil surface and changes in the amounts of water flowing from macropores were simulated using the Tires/tracks And Soil Compaction (TASC) tool and the MACRO model, respectively. Taking a 65 kW tractor on a clay loam as a reference, results showed that an increase in slip of the rear wheels from 1% to 27% caused normal stress to increase from 90.6 kPa to 104.4 kPa at the topsoil level, and the maximum shear contact stress to rise drastically from 6.0 kPa to 61.6 kPa. At 27% slip, topsoil was sheared and displaced over a distance of 0.35 m. Excessive normal and shear stress values with high slip caused severe reductions of the soil’s macroporosity, saturated hydraulic conductivity, and water quantities flowing from topsoil macropores. Assuming that, under conditions of intense rainfall on sloping land, a loss in vertical water flow would mean an increase in surface runoff, we calculated that a rainfall intensity of 100 mm h-1 and a rainfall duration of 1 h would increase the runoff coefficient to 0.79 at low slip and to 1.00 at high slip, indicating that 100% of rainwater would be transformed into surface runoff at high slip. We expect that these effects have a significant impact on soil erosion and floods in steeper terrain (slope > 15°) and across larger surface areas (> 16 m2) than those included in our study.

Potential desiccation cracks on Mars: A synthesis from modeling, analogue-field studies, and global observations

Potential desiccation polygons (PDPs) are polygonal surface patterns that are a common feature in Noachian-to-Hesperian-aged phyllosilicate- and chloride-bearing terrains and have been observed with size scales that range from cm-wide (by current rovers) to 10s of meters-wide. The global distribution of PDPs shows that they share certain traits in terms of morphology and geologic setting that can aid identification and distinction from fracturing patterns caused by other processes. They are mostly associated with sedimentary deposits that display spectral evidence for the presence of Fe/Mg smectites, Al-rich smectites or less commonly kaolinites, carbonates, and sulfates. In addition, PDPs may indicate paleolacustrine environments, which are of high interest for planetary exploration, and their presence implies that the fractured units are rich in smectite minerals that may have been deposited in a standing body of water. A collective synthesis with new data, particularly from the HiRISE camera suggests that desiccation cracks may be more common on the surface of Mars than previously thought. A review of terrestrial research on desiccation processes with emphasis on the theoretical background, field studies, and modeling constraints is presented here as well and shown to be consistent with and relevant to certain polygonal patterns on Mars.

Impact of local endothelial shear stress on neointima and plaque following stent implantation in patients with ST-elevation myocardial infarction: A subgroup-analysis of the COMFORTABLE AMI-IBIS 4 trial.

BACKGROUND Numerous studies have demonstrated an association between endothelial shear stress (ESS) and neointimal formation after stent implantation. However, the role of ESS on the composition of neointima and underlying plaque remains unclear. METHODS Patients recruited in the Comfortable AMI-IBIS 4 study implanted with bare metal stents (BMS) or biolimus eluting stents (BES) that had biplane coronary angiography at 13month follow-up were included in the analysis. The intravascular ultrasound virtual-histology (IVUS-VH) and the angiographic data were used to reconstruct the luminal surface, and the stent in the stented segments. Blood flow simulation was performed in the stent surface, which was assumed to represent the luminal surface at baseline, to assess the association between ESS and neointima thickness. The predominant ESS was estimated in 3-mm segments and was correlated with the amount of neointima, neointimal tissue composition, and with the changes in the underlying plaque burden and composition. RESULTS Forty three patients (18 implanted with BMS and 25 with BES) were studied. In both stent groups negative correlations were noted between ESS and neointima thickness in BMS (P<0.001) and BES (P=0.002). In BMS there was a negative correlation between predominant ESS and the percentage of the neointimal necrotic core component (P=0.015). In BES group, the limited neointima formation did not allow evaluation of the effect of ESS on its tissue characteristics. ESS did not affect vessel wall remodeling and the plaque burden and composition behind BMS (P>0.10) and BES (P>0.45). CONCLUSIONS ESS determines neointimal formation in both BMS and BES and affects the composition of the neointima in BMS. Conversely, ESS does not impact the plaque behind struts irrespective of stent type throughout 13months of follow-up.

Small quantity but large effect — How minor phases control strain localization in upper mantle shear zones

Low viscosity domains such as localized shear zones exert an important control on the geodynamics of the uppermost mantle. Grain size reduction and subsequent strain localization related to a switch from dislocation to diffusion creep is one mechanism to form low viscosity domains. To sustain strain localization, the grain size of mantle minerals needs to be kept small over geological timescales. One way to keep olivine grain sizes small is by pinning of mobile grain boundaries during grain growth by other minerals (second phases). Detailed microstructural studies based on natural samples from three shear zones formed at different geodynamic settings, allowed the derivation of the olivine grain-size dependence on the second-phase content. The polymineralic olivine grain-size evolution with increasing strain is similar in the three shear zones. If the second phases are to pin the mobile olivine grain boundary the phases need to be well mixed before grain growth. We suggest that melt-rock and metamorphic reactions are crucial for the initial phase mixing in mantle rocks. With ongoing deformation and increasing strain, grain boundary sliding combined with mass transfer processes and nucleation of grains promotes phase mixing resulting in fine-grained polymineralic mixtures that deform by diffusion creep. Strain localization due to the presence of volumetrically minor minerals in polymineralic mantle rocks is only important at high strain deformation (ultramylonites) at low temperatures (<~800°C). At smaller strain and stress conditions and/or higher temperatures other parameters like overall energy available to deform a given rock volume, the inheritance of mechanical anisotropies or the presence of water or melts needs to be considered to explain strain localization in the upper mantle.

P-T-t estimation of syn-kinematic strain in low-grade quartz-feldspar bearing rocks using thermodynamic modeling and 40Ar/39Ar dating techniques: example of the Plan-de-Phasy shear zone unit (Briançonnais Zone, Western Alps)

Pressure–Temperature–time (P–T–t) estimates of the syn-kinematic strain at the peak-pressure conditions reached during shallow underthrusting of the Briançonnais Zone in the Alpine subduction zone was made by thermodynamic modelling and 40Ar/39Ar dating in the Plan-de-Phasy unit (SE of the Pelvoux Massif, Western Alps). The dated phengite minerals crystallized syn-kinematically in a shear zone indicating top-to-the-N motion. By combining X-ray mapping with multi-equilibrium calculations, we estimate the phengite crystallization conditions at 270 ± 50 °C and 8.1 ± 2 kbar at an age of 45.9 ± 1.1 Ma. Combining this P–T–t estimate with data from the literature allows us to constrain the timing and geometry of Alpine continental subduction. We propose that the Briançonnais units were scalped on top of the slab during ongoing continental subduction and exhumed continuously until collision.

Structural, metamorphic and geochronological relations between the Zanskar Shear Zone and the Miyar Shear Zone (NW Indian Himalaya): Evidence for two distinct tectonic structures and implications for the evolution of the High Himalayan Crystalline of Zanskar

The geologic structures and metamorphic zonation of the northwestern Indian Himalaya contrast significantly with those in the central and eastern parts of the range, where the high-grade metamorphic rocks of the High Himalayan Crystalline (HHC) thrust southward over the weakly metamorphosed sediments of the Lesser Himalaya along the Main Central Thrust (MCT). Indeed, the hanging wall of the MCT in the NW Himalaya mainly consists of the greenschist facies metasediments of the Chamba zone, whereas HHC high-grade rocks are exposed more internally in the range as a large-scale dome called the Gianbul dome. This Gianbul dome is bounded by two oppositely directed shear zones, the NE-dipping Zanskar Shear Zone (ZSZ) on the northern flank and the SW-dipping Miyar Shear Zone (MSZ) on the southern limb. Current models for the emplacement of the HHC in NW India as a dome structure differ mainly in terms of the roles played by both the ZSZ and the MSZ during the tectonothermal evolution of the HHC. In both the channel flow model and wedge extrusion model, the ZSZ acts as a backstop normal fault along which the high-grade metamorphic rocks of the HHC of Zanskar are exhumed. In contrast, the recently proposed tectonic wedging model argues that the ZSZ and the MSZ correspond to one single detachment system that operates as a subhorizontal backthrust off of the MCT. Thus, the kinematic evolution of the two shear zones, the ZSZ and the MSZ, and their structural, metamorphic and chronological relations appear to be diagnostic features for discriminating the different models. In this paper, structural, metamorphic and geochronological data demonstrate that the MSZ and the ZSZ experienced two distinct kinematic evolutions. As such, the data presented in this paper rule out the hypothesis that the MSZ and the ZSZ constitute one single detachment system, as postulated by the tectonic wedging model. Structural, metamorphic and geochronological data are used to present an alternative tectonic model for the large-scale doming in the NW Indian Himalaya involving early NE-directed tectonics, weakness in the upper crust, reduced erosion at the orogenic front and rapid exhumation along both the ZSZ and the MSZ.

Geometry and kinematics of the Roisan-Cignana Shear Zone, and the orogenic evolution of the Dent Blanche Tectonic System (Western Alps)

The Dent Blanche Tectonic System (DBTS) is a composite thrust sheet derived from the previously thinned passive Adriatic continental margin. A kilometric high-strain zone, the Roisan-Cignana Shear Zone (RCSZ) defines the major tectonic boundary within the DBTS and separates it into two subunits, the Dent Blanche s.s. nappe to the northwest and the Mont Mary nappe to the southeast. Within this shear zone, tectonic slices of Mesozoic and pre-Alpine meta-sediments became amalgamated with continental basement rocks of the Adriatic margin. The occurrence of high pressure assemblages along the contact between these tectonic slices indicates that the amalgamation occurred prior to or during the subduction process, at an early stage of the Alpine orogenic cycle. Detailed mapping, petrographic and structural analysis show that the Roisan-Cignana Shear Zone results from several superimposed Alpine structural and metamorphic stages. Subduction of the continental fragments is recorded by blueschist-facies deformation, whereas the Alpine collision is reflected by a greenschist facies overprint associated with the development of large-scale open folds. The postnappe evolution comprises the development of low-angle brittle faults, followed by large-scale folding (Vanzone phase) and finally brittle extensional faults. The RCSZ shows that fragments of continental crust had been torn off the passive continental margin prior to continental collision, thus recording the entire history of the orogenic cycle. The role of preceding Permo-Triassic lithospheric thinning, Jurassic rifting, and ablative subduction processes in controlling the removal of crustal fragments from the reactivated passive continental margin is discussed. Results of this study constrain the temporal sequence of the tectono-metamorphic processes involved in the assembly of the DBTS, but they also show limits on the interpretation. In particular it remains difficult to judge to what extent precollisional rifting at the Adriatic continental margin preconditioned the efficiency of convergent processes, i.e. accretion, subduction, and orogenic exhumation.