A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Changes in species composition in alpine snowbeds with climate change inferred from small-scale spatial patterns

Alpine snowbeds are characterised by a very short growing season. However, the length of the snow-free period is increasingly prolonged due to climate change, so that snowbeds become susceptible to invasions from neighbouring alpine meadow communities. We hypothesised that spatial distribution of species generated by plant interactions may indicate whether snowbed species will coexist with or will be out-competed by invading alpine species – spatial aggregation or segregation will point to coexistence or competitive exclusion, respectively. We tested this hypothesis in snowbeds of the Swiss Alps using the variance ratio statistics. We focused on the relationships between dominant snowbed species, subordinate snowbed species, and potentially invading alpine grassland species. Subordinate snowbed species were generally spatially aggregated with each other, but were segregated from alpine grassland species. Competition between alpine grassland and subordinate snowbed species may have caused this segregation. Segregation between these species groups increased with earlier snowmelt, suggesting an increasing importance of competition with climate change. Further, a dominant snowbed species (Alchemilla pentaphyllea) was spatially aggregated with subordinate snowbed species, while two other dominants (Gnaphalium supinum and Salix herbacea) showed aggregated patterns with alpine grassland species. These dominant species are known to show distinct microhabitat preferences suggesting the existence of hidden microhabitats with different susceptibility to invaders. These results allow us to suggest that alpine snowbed areas are likely to be reduced as a consequence of climate change and that invading species from nearby alpine grasslands could outcompete subordinate snowbed species. On the other hand, microhabitats dominated by Gnaphalium or Salix seem to be particularly prone to invasions by non-snowbed species.

Experimental study of electric breakdowns in liquid argon at centimeter scale

In this paper we present results on measurements of the dielectric strength of liquid argon near its boiling point and cathode-anode distances in the range of 0.1 mm to 40 mm with spherical cathode and plane anode. We show that at such distances the applied electric field at which breakdowns occur is as low as 40 kV/cm. Flash-overs across the ribbed dielectric of the high voltage feed-through are observed for a length of 300 mm starting from a voltage of 55 kV. These results contribute to set reference for the breakdown-free design of ionization detectors, such as Liquid Argon Time Projection Chambers (LAr TPC).

Continental-Scale Footprint of Balancing and Positive Selection in a Small Rodent (Microtus arvalis)

Genetic adaptation to different environmental conditions is expected to lead to large differences between populations at selected loci, thus providing a signature of positive selection. Whereas balancing selection can maintain polymorphisms over long evolutionary periods and even geographic scale, thus leads to low levels of divergence between populations at selected loci. However, little is known about the relative importance of these two selective forces in shaping genomic diversity, partly due to difficulties in recognizing balancing selection in species showing low levels of differentiation. Here we address this problem by studying genomic diversity in the European common vole (Microtus arvalis) presenting high levels of differentiation between populations (average FST = 0.31). We studied 3,839 Amplified Fragment Length Polymorphism (AFLP) markers genotyped in 444 individuals from 21 populations distributed across the European continent and hence over different environmental conditions. Our statistical approach to detect markers under selection is based on a Bayesian method specifically developed for AFLP markers, which treats AFLPs as a nearly codominant marker system, and therefore has increased power to detect selection. The high number of screened populations allowed us to detect the signature of balancing selection across a large geographic area. We detected 33 markers potentially under balancing selection, hence strong evidence of stabilizing selection in 21 populations across Europe. However, our analyses identified four-times more markers (138) being under positive selection, and geographical patterns suggest that some of these markers are probably associated with alpine regions, which seem to have environmental conditions that favour adaptation. We conclude that despite favourable conditions in this study for the detection of balancing selection, this evolutionary force seems to play a relatively minor role in shaping the genomic diversity of the common vole, which is more influenced by positive selection and neutral processes like drift and demographic history.

Simple measures of climate, soil properties and plant traits predict national-scale grassland soil carbon stocks

Soil carbon (C) storage is a key ecosystem service. Soil C stocks play a vital role in soil fertility and climate regulation, but the factors that control these stocks at regional and national scales are unknown, particularly when their composition and stability are considered. As a result, their mapping relies on either unreliable proxy measures or laborious direct measurements. Using data from an extensive national survey of English grasslands, we show that surface soil (0–7 cm) C stocks in size fractions of varying stability can be predicted at both regional and national scales from plant traits and simple measures of soil and climatic conditions. Soil C stocks in the largest pool, of intermediate particle size (50–250 μm), were best explained by mean annual temperature (MAT), soil pH and soil moisture content. The second largest C pool, highly stable physically and biochemically protected particles (0·45–50 μm), was explained by soil pH and the community abundance-weighted mean (CWM) leaf nitrogen (N) content, with the highest soil C stocks under N-rich vegetation. The C stock in the small active fraction (250–4000 μm) was explained by a wide range of variables: MAT, mean annual precipitation, mean growing season length, soil pH and CWM specific leaf area; stocks were higher under vegetation with thick and/or dense leaves. Testing the models describing these fractions against data from an independent English region indicated moderately strong correlation between predicted and actual values and no systematic bias, with the exception of the active fraction, for which predictions were inaccurate. Synthesis and applications. Validation indicates that readily available climate, soils and plant survey data can be effective in making local- to landscape-scale (1–100 000 km2) soil C stock predictions. Such predictions are a crucial component of effective management strategies to protect C stocks and enhance soil C sequestration.

Description and repeatability of a newly developed spinal cord injury scale for dogs.

The objectives of this study were to describe a new spinal cord injury scale for dogs, evaluate repeatability through determining inter-rater variability of scores, compare these scores to another established system (a modified Frankel scale), and determine if the modified Frankel scale and the newly developed scale were useful as prognostic indicators for return to ambulation. A group of client-owned dogs with spinal cord injury were examined by 2 independent observers who applied the new Texas Spinal Cord Injury Score (TSCIS) and a modified Frankel scale that has been used previously. The newly developed scale was designed to describe gait, postural reactions and nociception in each limb. Weighted kappa statistics were utilized to determine inter-rater variability for the modified Frankel scale and individual components of the TSCIS. Comparisons were made between raters for the overall TSCIS score and between scales using Spearman's rho. An additional group of dogs with surgically treated thoracolumbar disk herniation was enrolled to look at correlation of both scores with spinal cord signal characteristics on magnetic resonance imaging (MRI) and ambulatory outcome at discharge. The actual agreement between raters for the modified Frankel scale was 88%, with a weighted kappa value of 0.93. The TSCIS had weighted kappa scores for gait, proprioceptive positioning and nociception components that ranged from 0.72 to 0.94. Correlation between raters for the overall TSCIS score was Spearman's rho=0.99 (P<0.001). Comparison of the overall TSCIS score to the modified Frankel score resulted in a Spearman's rho value of 0.90 (P<0.001). The modified Frankel score was weakly correlated with the length of hyperintensity of the spinal cord: L2 vertebral body length ratio on mid-sagittal T2-weighted MRI (Spearman's rho=-0.45, P=0.042) as was the overall TSCIS score (Spearman's rho=-0.47, P=0.037). There was also a significant difference in admitting modified Frankel scores (P=0.029) and admitting overall TSCIS scores (P=0.02) between dogs that were ambulatory at discharge and those that were not. Results from this study suggest that the TSCIS is an easy to administer scale for evaluating canine spinal cord injury based on the standard neurological exam and correlates well with a previously described modified Frankel scale.