Micromechanical study of elastic moduli of loose granular materials

In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential directions. It is well-known that mean-field theory gives inaccurate micromechanical predictions of the elastic moduli, especially for loose systems with low coordination number. Improved predictions of the moduli are obtained here for loose two-dimensional, isotropic assemblies. This is achieved by determining approximate displacement and rotation fields from the force and moment equilibrium conditions for small sub-assemblies of various sizes. It is assumed that the outer particles of these sub-assemblies move according to the mean field. From the particle displacement and rotation fields thus obtained, approximate elastic moduli are determined. The resulting predictions are compared with the true moduli, as determined from the discrete element method simulations for low coordination numbers and for various values of the tangential stiffness (at fixed value of the normal stiffness). Using this approach, accurate predictions of the moduli are obtained, especially when larger sub-assemblies are considered. As a step towards an analytical formulation of the present approach, it is investigated whether it is possible to replace the local contact stiffness matrices by a suitable average stiffness matrix. It is found that this generally leads to a deterioration of the accuracy of the predictions. Many micromechanical studies predict that the macroscopic bulk modulus is hardly influenced by the value of the tangential stiffness. It is shown here from the discrete element method simulations of hydrostatic compression that for loose systems, the bulk modulus strongly depends on the stiffness ratio for small stiffness ratios

On the elastic moduli of three-dimensional assemblies of spheres: characterization and modeling of fluctuations in the particle displacement and rotation

The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and lubrication. The mechanical properties of the samples are found to change with the preparation history, and to depend much more on coordination number than on density. Secondly, the fluctuations in the particle displacements from the average strain are analysed, and the way they affect the macroscopic behavior analyzed. It is found that only the average over equally oriented contacts of the relative displacement these fluctuations induce is relevant at the macroscopic scale. This average depends on coordination number, average geometry of the contact network and average contact stiffness. As far as the separate contributions from particle displacements and rotations are concerned, the former is found to counteract the average strain along the contact normal, while the latter do in the tangential plane. Conversely, the tangential components of the center displacements mainly arise to enforce local equilibrium, and have a small, and generally stiffening effect at the macro-scale. Finally, the fluctuations and the shear modulus that result from two approaches available in the literature are estimated numerically. These approaches are both based on the equilibrium of a small-sized representative assembly. The improvement of these estimate with respect to the average strain assumption indicates that the fluctuations relevant to the macroscopic behavior occur with short correlation length.Comment: Submitted to IJS

A Mesozoic bird from Gondwana preserving feathers

The fossil record of birds in the Mesozoic of Gondwana is mostly based on isolated and often poorly preserved specimens, none of which has preserved details on feather anatomy. We provide the description of a fossil bird represented by a skeleton with feathers from the Early Cretaceous of Gondwana (NE Brazil). The specimen sheds light on the homology and 3D structure of the rachis-dominated feathers, previously known from two-dimensional slabs. The rectrices exhibit a row of rounded spots, probably corresponding to some original colour pattern. The specimen supports the identification of the feather scapus as the rachis, which is notably robust and elliptical in cross-section. In spite of its juvenile nature, the tail plumage resembles the feathering of adult individuals of modern birds. Documentation of rachis-dominated tail in South American enantiornithines broadens the paleobiogeographic distribution of basal birds with this tail feather morphotype, up to now only reported from China.Fil: De Souza Carvalho, Ismar. Universidade Federal do Rio de Janeiro; BrasilFil: Novas, Fernando Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Agnolin, Federico. Universidad Maimónides; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Isasi, Marcelo Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentina. Universidad Maimónides; ArgentinaFil: Freitas, Francisco I.. Geopark Araripe; BrasilFil: Andrade, José A.. No especifíca

Internal states of model isotropic granular packings. III. Elastic properties

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page

Theropod Fauna from Southern Australia Indicates High Polar Diversity and Climate-Driven Dinosaur Provinciality

The Early Cretaceous fauna of Victoria, Australia, provides unique data on the composition of high latitude southern hemisphere dinosaurs. We describe and review theropod dinosaur postcranial remains from the Aptian–Albian Otway and Strzelecki groups, based on at least 37 isolated bones, and more than 90 teeth from the Flat Rocks locality. Several specimens of medium- and large-bodied individuals (estimated up to ∼8.5 metres long) represent allosauroids. Tyrannosauroids are represented by elements indicating medium body sizes (∼3 metres long), likely including the holotype femur of Timimus hermani, and a single cervical vertebra represents a juvenile spinosaurid. Single specimens representing medium- and small-bodied theropods may be referrable to Ceratosauria, Ornithomimosauria, a basal coelurosaur, and at least three taxa within Maniraptora. Thus, nine theropod taxa may have been present. Alternatively, four distinct dorsal vertebrae indicate a minimum of four taxa. However, because most taxa are known from single bones, it is likely that small-bodied theropod diversity remains underestimated. The high abundance of allosauroids and basal coelurosaurs (including tyrannosauroids and possibly ornithomimosaurs), and the relative rarity of ceratosaurs, is strikingly dissimilar to penecontemporaneous dinosaur faunas of Africa and South America, which represent an arid, lower-latitude biome. Similarities between dinosaur faunas of Victoria and the northern continents concern the proportional representatation of higher clades, and may result from the prevailing temperate–polar climate of Australia, especially at high latitudes in Victoria, which is similar to the predominant warm–temperate climate of Laurasia, but distinct from the arid climate zone that covered extensive areas of Gondwana. Most dinosaur groups probably attained a near-cosmopolitan distribution in the Jurassic, prior to fragmentation of the Pangaean supercontinent, and some aspects of the hallmark ‘Gondwanan’ fauna of South America and Africa may therefore reflect climate-driven provinciality, not vicariant evolution driven by continental fragmentation. However, vicariance may still be detected at lower phylogenetic levels

A semi-empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination-number and Poisson-ratio

The effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over-predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non-linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three-step modified grain contact theory model to a two-step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed