FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.     

Analysis of a cryolava flow-like feature on Titan

This paper reports on the analysis of the highest spatial resolution hyperspectral images acquired by the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft during its prime mission. A bright area matches a flow-like feature coming out of a caldera-like feature observed in Synthetic Aperture Radar (SAR) data recorded by the Cassini radar experiment [Lopes et al., 2007. Cryovolcanic features on Titan's surface as revealed by the Cassini Titan Radar Mapper. Icarus 186, 395-412, doi:10.1016/j.icarus.2006.09.006]. In this SAR image, the flow extends about 160 km east of the caldera. The contrast in brightness between the flow and the surroundings progressively vanishes, suggesting alteration or evolution of the composition of the cryolava during the lifetime of the eruptions. Dunes seem to cover part of this flow on its eastern end. We analyze the different terrains using the Spectral Mixing Analysis (SMA) approach of the Multiple-Endmember Linear Unmixing Model (MELSUM, Combe et al., 2008). The study area can be fully modeled by using only two types of terrains. Then, the VIMS spectra are compared with laboratory spectra of known materials in the relevant atmospheric windows (from 1 to 2.78 μm). We considered simple molecules that could be produced during cryovolcanic events, including H₂O, CO₂ (using two different grain sizes), CH₄ and NH₃. We find that the mean spectrum of the cryoflow-like feature is not consistent with pure water ice. It can be best fitted by linear combinations of spectra of the candidate materials, showing that its composition is compatible with a mixture of H₂O, CH₄ and CO_2.     

Vestan lithologies mapped by the visual and infrared spectrometer on Dawn

We present global lithological maps of the Vestan surface based on Dawn mission's Visible InfraRed (VIR) Spectrometer acquisitions with a spatial sampling of 200 m. The maps confirm the results obtained with the data set acquired by VIR with a spatial sampling of 700 m, that the reflectance spectra of Vesta's surface are dominated by pyroxene absorptions that can be interpreted within the context of the distribution of howardites, eucrites, and diogenites (HEDs). The maps also partially agree with the ground and Hubble Space Telescope observations: they confirm the background surface being an assemblage of howardite or polymict eucrite, as well as the location of a diogenitic‐rich spot; however, there is no evidence of extended olivine‐rich regions in the equatorial latitudes. Diogenite is revealed on the Rheasilvia basin floor, indicating that material of the lower crust/mantle was exposed. VIR also detected diogenites along the scarp of Matronalia Rupes, and the rims of Severina and a nearby, unnamed crater, and as ejecta of Antonia crater. The diogenite distribution is fully consistent with petrological constraints; although the mapped distribution does not provide unambiguous constraints, it favors the hypothesis of a magma ocean.     

Dawn completes its mission at 4 Vesta

The Dawn mission was designed to test our hypothesis about the origin and evolution of the early solar system by visiting the largest differentiated basaltic asteroid, 4 Vesta, believed to be a survivor from the earliest times of rocky body formation. Observations from orbit show that Vesta is the parent body of the Howardite, Eucrite, Diogenite meteorites. Vesta has an iron core and a eucritic–diogenitic crust. Its surface is characterized by abundant impact craters but with no evident volcanic features. It has two ancient impact basins in the southern hemisphere that are associated with circum‐planetary troughs. The northern hemisphere is the more heavily cratered and contains the oldest terrains. The surface of Vesta is diverse, with north‐south and east‐west dichotomies in the eucrite‐to‐diogenite ratio. Its surface contains both very bright and very dark material, and its color varies strongly from region to region. Both the mineralogical and the elemental compositions agree with that expected for the HED parent body. Significant OH or H may be present in the upper crust and the presence of pits in “fresh” craters is consistent with the devolatilization of the surface after a collision either brought to or tapped a source of water on Vesta. The presence of dark material on the surface of Vesta suggests efficient transport pathways for organic material, and the mixing of the dark material with the more pristine pyroxene explains the varying albedo across the surface. Vesta has proven to be a reliable witness to the formation of the solar system.     

From discrete to continuum modelling of boundary value problems in geomechanics: An integrated FEM-DEM approach

Double-scale numerical methods constitute an effective tool for simultaneously representing the complex nature of geomaterials and treating real-scale engineering problems such as a tunnel excavation or a pressuremetre at a reasonable numerical cost. This paper presents an approach coupling discrete elements (DEM) at the microscale with finite elements (FEM) at the macroscale. In this approach, a DEM-based numerical constitutive law is embedded into a standard FEM formulation. In this regard, an exhaustive discussion is presented on how a 2D/3D granular assembly can be used to generate, step by step along the overall computation process, a consistent Numerically Homogenised Law. The paper also focuses on some recent developments including a comprehensive discussion of the efficiency of Newton-like operators, the introduction of a regularisation technique at the macroscale by means of a second gradient framework, and the development of parallelisation techniques to alleviate the computational cost of the proposed approach. Some real-scale problems taking into account the material spatial variability are illustrated, proving the numerical efficiency of the proposed approach and the benefit of a particle-based strategy.     

Experimental and discrete element modeling studies of the trapdoor problem: influence of the macro-mechanical frictional parameters

Granular soils have the inherent ability to develop load transfers in their mass. Mechanisms of load transfers are used as a basic principle of many civil and geotechnical engineering applications. However, their complexity makes it difficult to formulate relevant design methods for such works. The trapdoor problem is one of the ways to reproduce load transfers by the arching effect in a granular layer in non-complex conditions. In addition, many analytical solutions for the prediction of load transfer mechanisms are based on the trapdoor problem. However, some of the parameters required are still being widely discussed, in particular the ratio of horizontal stress to vertical stress. For this paper, an experimental device for trapdoor tests in plane strain conditions was created and several geomaterials were tested. Three phases in the response of the materials were consistently observed. Each of these phases corresponded to a specific displacement of the trapdoor. A first phase of high load transfer was observed followed by a transition phase which was followed by a critical phase for which the load transfer amplitude increased and stabilized. Analytical solutions and experimental values of load transfers were compared. Considerable differences between the stress ratio needed to fit the experimental data and the stress ratio proposed in the analytical models were noted. Based on the conclusions of the experimental study, the discrete element method was used to model the same trapdoor problem. A wide range of granular materials was modeled and tested in the trapdoor problem. The three phases in the response of the layer were also observed in the numerical modeling. In addition, it was shown that the shear strength of the material is the key parameter of load transfers: peak shear resistance for the small displacements of the trapdoor and critical shear strength for the larger displacements. A micro-mechanical analysis showed that the effective stress ratio in the sheared zone does not vary as much with shear strength. Stress ratios here were again greater than those proposed in the analytical solutions. Nevertheless, the relevance of the solution of Terzaghi was confirmed as soon as the stress ratio was correctly chosen.     

Photometric correction and in-flight calibration of Chang’ E-1 Interference Imaging Spectrometer (IIM) data

The main objective of this study is to develop a new photometric correction that is suitable for global Chang’ E-1 (CE-1) Interference Imaging Spectrometer (IIM) data. We considered two improvements in the accuracy of the photometric correction: (1) classifying the whole Moon’s surface into four classes (very bright rays, mature highlands, low FeO basalts, and high FeO basalts) based on the FeO contents; (2) decoupling the combined effects of the solar photometry and the detector responsivity along the cross-track. The results showed that our decoupling method could correct the non-uniformity of detector response but retain the cross-track photometry. Based on these in-flight calibrated data, spectrally continuous photometric functions of the four classes were obtained. By eliminating the contamination from highlands ejecta and low FeO basalts, the opposition surge of the high FeO maria was evident for the first time. The amplitude and width of the opposition surge presents wavelength dependence, which suggests that shadow hiding is the mechanism responsible for the opposition surge. A global lunar reflectance map whose boundaries between adjacent orbits are invisible was generated using the new four-type photometric functions. The quality of the global mosaic and the consistency of the reflectance spectra of the same area obtained in different orbits indicate the effectiveness of our photometric correction method. Although our method was specifically applied to the IIM data, the photometric correction method and the parameter values derived in this study is expected to be suitable for other optical instruments.     

The Circum-Hellas Volcanic Province,Mars: Overview

Building on previous studies of volcanoes around the Hellas basin with new studies of imaging (High-Resolution Stereo Camera (HRSC), Thermal Emission Imaging System (THEMIS), Mars Orbiter Camera (MOC), High-Resolution Imaging Science Experiment (HiRISE), Context Imager (CTX)), multispectral (HRSC, Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA)), topographic (Mars Orbiter Laser Altimeter (MOLA)) and gravity data, we define a new Martian volcanic province as the Circum-Hellas Volcanic Province (CHVP). With an area of >2.1 million km², it contains the six oldest central vent volcanoes on Mars, which formed after the Hellas impact basin, between 4.0 and 3.6 Ga. These volcanoes mark a transition from the flood volcanism that formed Malea Planum ～3.8 Ga, to localized edifice-building eruptions. The CHVP volcanoes have two general morphologies: (1) shield-like edifices (Tyrrhena, Hadriaca, and Amphitrites Paterae), and (2) caldera-like depressions surrounded by ridged plains (Peneus, Malea, and Pityusa Paterae). Positive gravity anomalies are found at Tyrrhena, Hadriaca, and Amphitrites, perhaps indicative of dense magma bodies below the surface. The lack of positive-relief edifices and weak gravity anomalies at Peneus, Malea, and Pityusa suggest a fundamental difference in their formation, styles of eruption, and/or compositions. The northernmost volcanoes, the ～3.7–3.9 Ga Tyrrhena and Hadriaca Paterae, have low slopes, well-channeled flanks, and smooth caldera floors (at tens of meters/pixel scale), indicative of volcanoes formed from poorly consolidated pyroclastic deposits that have been modified by fluvial and aeolian erosion and deposition. The ～3.6 Ga Amphitrites Patera also has a well-channeled flank, but it and the ～3.8 Ga Peneus Patera are dominated by scalloped and pitted terrain, pedestal and ejecta flow craters, and a general ‘softened’ appearance. This morphology is indicative not only of surface materials subjected to periglacial processes involving water ice, but also of a surface composed of easily eroded materials such as ash and dust. The southernmost volcanoes, the ～3.8 Ga Malea and Pityusa Paterae, have no channeled flanks, no scalloped and pitted terrain, and lack the ‘softened’ appearance of their surfaces, but they do contain pedestal and ejecta flow craters and large, smooth, bright plateaus in their central depressions. This morphology is indicative of a surface with not only a high water ice content, but also a more consolidated material that is less susceptible to degradation (relative to the other four volcanoes). We suggest that Malea and Pityusa (and possibly Peneus) Paterae are Martian equivalents to Earth's giant calderas (e.g., Yellowstone, Long Valley) that erupted large volumes of volcanic materials, and that Malea and Pityusa are probably composed of either lava flows or ignimbrites. HRSC and OMEGA spectral data indicate that dark gray to slightly red materials (often represented as blue or black pixels in HRSC color images), found in the patera floors and topographic lows throughout the CHVP, have a basaltic composition. A key issue is whether this dark material represents concentrations of underlying basaltic material eroded by various processes and exposed by aeolian winnowing, or if the material was transported from elsewhere on Mars by regional winds. Understanding the provenance of these dark materials may be the key to understanding the volcanic diversity of the Circum-Hellas Volcanic Province.     

Titan's surface: Search for spectral diversity and composition using the Cassini VIMS investigation

The surface composition of Titan is of great importance for understanding both the internal evolution of Titan and its atmosphere. The Visual and Infrared Mapping Spectrometer (VIMS) investigation on Cassini is observing Titan from 0.35 to 5.11 μm with spatial resolution down to a few kilometers during each flyby of the spacecraft as it orbits Saturn. Our search for spectral diversity using seven methane transmission windows in the near infrared suggests that spectrally distinct units exist on the surface of Titan and that most of the surface can be modeled using only a few distinct spectral units: water frost, CO₂ frost, atmospheric scattering, and an unknown material bright at 2 μm. A dark, spectrally neutral material is also implied. Use of an atmospheric scattering component with spectral mixing analysis may provide a method for partially removing atmospheric effects. In some locations, atmospheric scattering accounts for the majority of the signal. There are also small regions with unusual spectra that may be due to low signal and high noise and/or may be exotic materials of interest. Further, we searched within the methane windows for spectral features associated with Titan's surface. Only the 5-μm and, to a lesser extent, the 2-μm window provide a reasonable opportunity for this, as the shorter-wavelength windows are too narrow and the 2.8-μm window is cluttered with an unknown atmospheric constituent. We find evidence for only one spectral feature: near 4.92 μm for the 5-μm bright Tui Regio region. CO₂ frost with grains smaller than about 10 μm is the best candidate we have found so far to explain this absorption as well as the feature's spectral contrast between the 2.7- and the 2.8-μm atmosphere subwindows. This suggested CO₂ identification is supported by the presence of an endmember in the spectral mixture analysis that is consistent with CO₂ frost with large grain sizes. We find no other absorption features that are statistically significant, including those reported earlier by others. These results are consistent with but greatly extend our early analysis that treated only the Ta data set [McCord, T.B., et al., 2006a. Planet. Space Sci. 54, 1524-1539]. In the spectral feature search process, we explored in detail the noise characteristics of the VIMS data within the 5-μm window, which has generally very low signal (4-20 DN), due to the measurement conditions and low illumination levels. We find noise of nearly Gaussian statistics except for some erratic darks and noise spikes, and the data set seems generally well behaved. We present examples of our attempt to improve on the standard VIMS pipeline data calibration.