Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Comparison of theoretical fixation stability of three devices employed in medial opening wedge high tibial osteotomy: a finite element analysis.

BACKGROUND Medial open wedge high tibial osteotomy is a well-established procedure for the treatment of unicompartmental osteoarthritis and symptomatic varus malalignment. We hypothesized that different fixation devices generate different fixation stability profiles for the various wedge sizes in a finite element (FE) analysis. METHODS Four types of fixation were compared: 1) first and 2) second generation Puddu plates, and 3) TomoFix plate with and 4) without bone graft. Cortical and cancellous bone was modelled and five different opening wedge sizes were studied for each model. Outcome measures included: 1) stresses in bone, 2) relative displacement of the proximal and distal tibial fragments, 3) stresses in the plates, 4) stresses on the upper and lower screw surfaces in the screw channels. RESULTS The highest load for all fixation types occurred in the plate axis. For the vast majority of the wedge sizes and fixation types the shear stress (von Mises stress) was dominating in the bone independent of fixation type. The relative displacements of the tibial fragments were low (in μm range). With an increasing wedge size this displacement tended to increase for both Puddu plates and the TomoFix plate with bone graft. For the TomoFix plate without bone graft a rather opposite trend was observed.For all fixation types the occurring stresses at the screw-bone contact areas pulled at the screws and exceeded the allowable threshold of 1.2 MPa for at least one screw surface. Of the six screw surfaces that were studied, the TomoFix plate with bone graft showed a stress excess of one out of twelve and without bone graft, five out of twelve. With the Puddu plates, an excess stress occurred in the majority of screw surfaces. CONCLUSIONS The different fixation devices generate different fixation stability profiles for different opening wedge sizes. Based on the computational simulations, none of the studied osteosynthesis fixation types warranted an intransigent full weight bearing per se. The highest fixation stability was observed for the TomoFix plates and the lowest for the first generation Puddu plate. These findings were revealed in theoretical models and need to be validated in controlled clinical settings.

A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy

Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last Interglacial–Glacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic Dansgaard–Oeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (δ18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of Dansgaard–Oeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.

Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fracture is a common medical problem in osteoporotic individuals. The quantitative computed tomography (QCT)-based finite element (FE) method may be used to predict vertebral strength in vivo, but needs to be validated with experimental tests. The aim of this study was to validate a nonlinear anatomy specific QCT-based FE model by using a novel testing setup. Thirty-seven human thoracolumbar vertebral bone slices were prepared by removing cortical endplates and posterior elements. The slices were scanned with QCT and the volumetric bone mineral density (vBMD) was computed with the standard clinical approach. A novel experimental setup was designed to induce a realistic failure in the vertebral slices in vitro. Rotation of the loading plate was allowed by means of a ball joint. To minimize device compliance, the specimen deformation was measured directly on the loading plate with three sensors. A nonlinear FE model was generated from the calibrated QCT images and computed vertebral stiffness and strength were compared to those measured during the experiments. In agreement with clinical observations, most of the vertebrae underwent an anterior wedge-shape fracture. As expected, the FE method predicted both stiffness and strength better than vBMD (R2 improved from 0.27 to 0.49 and from 0.34 to 0.79, respectively). Despite the lack of fitting parameters, the linear regression of the FE prediction for strength was close to the 1:1 relation (slope and intercept close to one (0.86 kN) and to zero (0.72 kN), respectively). In conclusion, a nonlinear FE model was successfully validated through a novel experimental technique for generating wedge-shape fractures in human thoracolumbar vertebrae.

Fluid-related inclusions in Alpine high-pressure peridotite reveal trace element recycling during subduction-zone dehydration of serpentinized mantle (Cima di Gagnone, Swiss Alps).

Serpentinites release at sub-arc depths volatiles and several fluid-mobile trace elements found in arc magmas. Constraining element uptake in these rocks and defining the trace element composition of fluids released upon serpentinite dehydration can improve our understanding of mass transfer across subduction zones and to volcanic arcs. The eclogite-facies garnet metaperidotite and chlorite harzburgite bodies embedded in paragneiss of the subduction melange from Cima di Gagnone derive from serpentinized peridotite protoliths and are unique examples of ultramafic rocks that experienced subduction metasomatism and devolatilization. In these rocks, metamorphic olivine and garnet trap polyphase inclusions representing the fluid released during high-pressure breakdown of antigorite and chlorite. Combining major element mapping and laser-ablation ICP-MS bulk inclusion analysis, we characterize the mineral content of polyphase inclusions and quantify the fluid composition. Silicates, Cl-bearing phases, sulphides, carbonates, and oxides document post-entrapment mineral growth in the inclusions starting immediately after fluid entrapment. Compositional data reveal the presence of two different fluid types. The first (type A) records a fluid prominently enriched in fluid-mobile elements, with Cl, Cs, Pb, As, Sb concentrations up to 10(3) PM (primitive mantle), similar to 10(2) PM Tit Ba, while Rb, B, Sr, Li, U concentrations are of the order of 10(1) PM, and alkalis are similar to 2 PM. The second fluid (type B) has considerably lower fluid-mobile element enrichments, but its enrichment patterns are comparable to type A fluid. Our data reveal multistage fluid uptake in these peridotite bodies, including selective element enrichment during seafloor alteration, followed by fluid-rock interaction along with subduction metamorphism in the plate interface melange. Here, infiltration of sediment-equilibrated fluid produced significant enrichment of the serpentinites in As, Sb, B, Pb, an enriched trace element pattern that was then transferred to the fluid released at greater depth upon serpentine dehydration (type A fluid). The type B fluid hosted by garnet may record the composition of the chlorite breakdown fluid released at even greater depth. The Gagnone study-case demonstrates that serpentinized peridotites acquire water and fluid-mobile elements during ocean floor hydration and through exchange with sediment-equilibrated fluids in the early subduction stages. Subsequent antigorite devolatilization at subarc depths delivers aqueous fluids to the mantle wedge that can be prominently enriched in sediment-derived components, potentially triggering arc magmatism without the need of concomitant dehydration/melting of metasediments or altered oceanic crust.

Major and trace element compositions of the Buendnerschiefer samples

The Bündnerschiefer of the Swiss-Italian Alps is a large sedimentary complex deposited on the Piemonte-Liguria and Valais oceans and associated continental margins from the upper Jurassic to Eocene. It is made of a large variety of sequences associated or not with an ophiolitic basement. The Bündnerschiefer makes an accretionary prism that developed syn-tectonically from the onset of alpine subduction, and it records orogenic metamorphism following episodes of HP metamorphism. The Bündnerschiefer shares important similarities with the Otago schists of New Zealand and with the Wepawaug schists of Connecticut, both of which form accretionary prisms and have an orogenic metamorphic imprint. With the aim of testing the hypothesis of mobility of chemical components as a function of metamorphic grade, in this work I present fifty-five bulk chemical analyses of various lithological facies of the Bündnerschiefer collected along the well-studied field gradient of the Lepontine dome of Central Switzerland, in the Prättigau half window of East Switzerland, and in the Tsaté Nappe of Valle d'Aosta (Italy). The dataset includes the concentration of major components, large ion lithophile elements (Rb, Sr, Ba, Cs), high field strength elements (Zr, Ti, Nb, Th, U, Ta, Hf), fluid-mobile light elements (B, Li), volatiles (CO2, S), REEs, and Y, V, Cr, Co, Sn, Pb, Cu, Zn, Tl, Sb, Be, and Au. These data are compared against the compositions of the global marine sediment reservoir, typical crustal reservoirs, and against the previously measured compositions of Otago and Wepawaug schists. Results reveal that, irrespective of their metamorphic evolution, the bulk chemical compositions of orogenic metasediments are characterized by mostly constant compositional ratios (e.g., K2O/Al2O3, Ba/Al2O3, Sr/CaO, etc.), whose values in most cases are undistinguishable from those of actual marine sediments and other crustal reservoirs. For these rocks, only volatile concentrations decrease dramatically as a function of metamorphic temperature, and significant deviations from the reservoir signatures are evident for SiO2, B, and Li. These results are interpreted as an indication of residual enrichment in the sediments, a process taking place during syn-metamorphic dehydration from the onset of metamorphism in a regime of chemical immobility. Residual enrichment increased the absolute concentrations of the chemical components of these rocks, but did not modify significantly their fundamental ratios. This poor compositional modification of the sediments indicates that orogenic metamorphism in general does not promote significant mass transfer from accretionary prisms. In contrast, mass transfer calculations carried out in a shear zone crosscutting the Bündnerschiefer shows that significant mass transfer occurs within these narrow zones, resulting in gains of H2O, SiO2, Al2O3, K2O, Ba, Y, Rb, Cu, V, Tl, Mo, and Ce during deformation and loss of Na2O, CO2, S, Ni, B, U, and Pb from the rock. These components were presumably transported by an aquo-carbonic fluid along the shear zone. These distinct attitudes to mobilize chemical elements from orogenic sediments may have implications for a potentially large number of geochemical processes in active continental margins, from the recycling of chemical components at plate margins to the genesis of hydrothermal ore deposits.

Characteristics, pyrolysis, age, lithology, sedimentation rate, organic matter, and thermal alteration index at DSDP Leg 67 Holes

Marine-derived amorphous organic matter dominates hemipelagic and trench sediments in and around the Middle America Trench. These sediments contain, on the average, 1% to 2% total organic carbon (TOC), with a maximum of 4.8%. Their organic facies and richness reflect (1) the small land area of Guatemala, which contributes small amounts of higher land plant remains, and (2) high levels of marine productivity and regionally low levels of dissolved oxygen, which encourage deposition and preservation of marine organic remains. These sediments have good potential for oil but are now immature. For this reason, gaseous hydrocarbons like the ethane identified in the deep parts of the section, as at Sites 496 and 497, are probably migrating from a mature section at depth. The pelagic sediments of the downgoing Cocos Plate are lean in organic carbon and have no petroleum potential

Chemical element contents and accumulation rates in metalliferous sediments from DSDP Hole 34-319, Bauer Deep, Southeast Pacific

Marked variations in the chemical and mineralogical composition of sediments at Site 319 have occurred during the 15 My history of sedimentation at this site. The change in composition through time parallels the variability observed in surface sediments from various parts of the Nazca Plate and can be related to variations in the proportion of hydrothermal, hydrogenous, detrital and biogenous phases reaching this site at different times. Metal accumulation rates at Site 319 reach a maximum near the basement for most elements, suggesting a strong hydrothermal contribution during the early history of this site. The hydrothermal contribution decreased rapidly as Site 319 moved away from the spreading center, although a subtle increase in this source is detectable about the time spreading began on the East Pacific Rise. The most recent sedimentation exhibits a strong detritalhydrogenous influence. Post-depositional diagenesis of amorphous phases has converted them to ironrich smectite and well-crystallized goethite without significantly altering the bulk composition of the sediment.

Element oxides in basaltic glass fragments from ODP Hole 203-1243B

Sand-sized basaltic glass fragments were recovered in the liner of Core 203-1243B-19R, the deepest recovery from Hole 1243B. Microprobe analysis of 582 glassy cuttings cluster into five compositionally distinct groups, most of which are unlike the lithologic units described on board ship. Drilling operations intended to sweep cuttings from the caving hole and differences between the cuttings and geochemically distinct lithologic units of the upper part of the basement indicate that the cuttings came mainly, if not entirely, from the lower part of the hole. They give information about the part of Hole 1243B that had poor core recovery. Enriched mid-ocean-ridge basalt (MORB) from the upper part of the hole and transitional MORB from two groups of cuttings from sources low in the hole may be a trace of the Galápagos plume on the Pacific plate or may be a normal consequence of eruptions from two distinct magmas on fast-spreading crust.

Concentrations of major-element oxides and minor and trace elements at DSDP Legs 87, 57, 56 and 31

Sediments from Sites 582 (11 samples), 583 (19 samples), 584 (31 samples), 294 (1 sample), 296 (9 samples), 297 (3 samples), 436 (11 samples), and 439 (3 samples) were analyzed by X-ray fluorescence and/or instrumental neutron activation analysis. Ten major elements and 24 minor and trace elements (including 7 rare earth elements) were determined with these methods. Geochemistry varies systematically with both the site location and sediment age. Such variations are explained in terms of changes in sedimentation processes caused by plate motion and changes in ocean currents.

(Table 1) Isotopic and trace-element ratios of Emperor Seamount basalts

When a mantle plume interacts with a mid-ocean ridge, both are noticeably affected. The mid-ocean ridge can display anomalously shallow bathymetry, excess volcanism, thickened crust, asymmetric sea-floor spreading and a plume component in the composition of the ridge basalts (Schilling, 1973, doi:10.1038/242565a0; Verma et al., 1983, doi:10.1038/306654a0; Ito and Lin, 1995, doi:10.1130/0091-7613(1995)023<0657:OSCHIC>2.3.CO;2; Müller et al., 1998, doi:10.1038/24850). The hotspot-related volcanism can be drawn closer to the ridge, and its geochemical composition can also be affected (Ito and Lin, 1995, doi:10.1130/0091-7613(1995)023<0657:OSCHIC>2.3.CO;2; White et al., 1993, doi:10.1029/93JB02018; Kincaid et al., 1995, doi:10.1038/376758a0; Kingsley and Schilling, 1998, doi:10.1029/98JB01496 ). Here we present Sr-Nd-Pb isotopic analyses of samples from the next-to-oldest seamount in the Hawaiian hotspot track, the Detroit seamount at 51° N, which show that, 81 Myr ago, the Hawaiian hotspot produced volcanism with an isotopic signature indistinguishable from mid-ocean ridge basalt. This composition is unprecedented in the known volcanism from the Hawaiian hotspot, but is consistent with the interpretation from plate reconstructions (Mammerickx and Sharman, 1988, doi:10.1029/JB093iB04p03009) that the hotspot was located close to a mid-ocean ridge about 80 Myr ago. As the rising mantle plume encountered the hot, low-viscosity asthenosphere and hot, thin lithosphere near the spreading centre, it appears to have entrained enough of the isotopically depleted upper mantle to overwhelm the chemical characteristics of the plume itself. The Hawaiian hotspot thus joins the growing list of hotspots that have interacted with a rift early in their history.

Major element oxides and 40Ar/39Ar plateau and isochron ages of ODP Hole 165-1001A

40Ar-39Ar incremental heating experiments and electron microprobe analyses were performed on basaltic rocks recovered from Site 1001 during Ocean Drilling Program Leg 165. The lower Nicaraguan Rise, on which Site 1001 lies, appears to be part of a larger Caribbean oceanic plateau that makes up the core of the Caribbean plate. Our results indicate an eruption age of 81 ± 1 Ma. A single flow-rim glass is tholeiitic and almost identical to the shipboard X-ray fluorescence analyses of the whole rock. The slightly porphyritic basalts have at least two populations of plagioclase, groundmass, and glomerocrystic plagioclase laths that appear to be in equilibrium with the surrounding melt and corroded tabular phenocrysts that have a higher An content (An84-86).

U-Pb, trace element, and Hf isotope analysis for Macquarie Island detrital zircon

Oceanic zircon trace element and Hf-isotope geochemistry offers a means to assess the magmatic evolution of a dying spreading ridge and provides an independent evaluation of the reliability of oceanic zircon as an indicator of mantle melting conditions. The Macquarie Island ophiolite in the Southern Ocean provides a unique testing ground for this approach due to its formation within a mid-ocean ridge that gradually changed into a transform plate boundary. Detrital zircon recovered from the island records this change through a progressive enrichment in incompatible trace elements. Oligocene age (33-27 Ma) paleo-detrital zircon in ophiolitic sandstones and breccias interbedded with pillow basalt have trace element compositions akin to a MORB crustal source, whereas Late Miocene age (8.5 Ma) modern-detrital zircon collected from gabbroic colluvium on the island have highly enriched compositions unlike typical oceanic zircon. This compositional disparity between age populations is not complimented by analytically equivalent eHf data that primarily ranges from 14 to 13 for sandstone and modern-detrital populations. A wider compositional range for the sandstone population reflects a multiple pluton source provenance and is augmented by a single cobble clast with eHf equivalent to the maximum observed composition in the sandstone (~17). Similar sandstone and colluvium Hf-isotope signatures indicate inheritance from a similar mantle reservoir that was enriched from the depleted MORB mantle average. The continuity in Hf-isotope signature relative to trace element enrichment in Macquarie Island zircon populations, suggests the latter formed by reduced partial melting linked to spreading-segment shortening and transform lengthening along the dying spreading ridge.