Modeling and testing of snow penetration

Penetration by a cone into snow is commonly used to characterize snow properties. However, the effects of the diameter and half-angle of the cone on the mechanical properties of snow have not been systematically studied. In addition, no estimation of material parameters in a physically-based model has been made such that the results from penetration provide only an index of snow properties. In this paper, modeling and experimental methods are used to examine the effects of cone geometry on the maximum penetration force and associated hardness, with penetrometers ranging from 2.5 to 4 mm in diameter, 15° to 45° in cone half-angle, and testing both fine-grained and coarse-grained snows. The material point method, in conjunction with the Drucker–Prager cap plasticity model, was used to obtain the theoretical penetration force-distance relationship. Global sensitivity studies were conducted that indicate that the cohesion accounts for 86% of the penetration force, followed distantly by friction angle which accounts for 27%. A general trend, for the simulation results was established: for a given half-angle, the penetration force increases with the increase of diameter which holds for most of the test data as well; for a given diameter, the penetration force decreases with the increase of half-angle, which holds for some of the test data. In addition, for a given half-angle, the hardness decreases with the increase of diameter; for a given diameter, the hardness decreases with the increase of half-angle. To take into consideration the uncertainty of test data, a simple interval-based metric was used to compare test data with simulation results; the comparison was satisfactory. The material parameters from the simulations can thus be considered as calibrated ones for the snow studied.     

Vehicle-wet snow interaction: Testing,modeling and validation

For a vehicle interacting with snow, whether dry or wet, uncertainties exist in the mechanical properties of snow, and in the interfacial properties between the tires of the vehicle and snow. For dry snow, these uncertainties have been studied recently using methods within a statistical framework employing a simple stochastic tire-snow interaction model and several validation metrics. Wet snow is more complicated and much less studied than dry snow, especially for tire-snow interaction. In this paper, the authors used a physical tire-snow interaction model and a similar statistical framework as was used to analyze dry snow, and presented results of calibration and validation of the interaction model for wet snow in conjunction with new test data based on a single test run with the assumption that it would provide needed sampling points for statistical analysis. Four local and global statistical validation metrics were used to assess the physical and statistical models with good results. Comparison between wet and dry snow, based on a single test run, shows that the former has a lower interfacial coefficient of friction, and a higher drawbar pull than the latter.     

Statistical modeling and comparison with experimental data of tire–soil interaction for combined longitudinal and lateral slip

The interaction of a tire with a soft terrain has multiple sources of uncertainties such as the mechanical properties of the terrain, and the interfacial properties between the tire and the terrain. These uncertainties are best characterized using statistical methods such as the development of stochastic models of tire–soil interaction. The quality of the models can be assessed via statistical validation measures or metrics. Although validation of stochastic tire–soil interaction models has recently been reported with good results, it involves longitudinal slip only without considering lateral slip which can occur simultaneously with longitudinal motion. This paper presents results of the validation of a simple stochastic tire–soil interaction model for the more complicated case of combined slip. The statistical methods used for validation include the development of a Gaussian process metamodel, the calibration of model parameters using the approach of the maximum likelihood estimate in conjunction with new test data. The validation of the calibrated model, when compared with test data, is obtained using four validation metrics with good results.     

Détermination du critère de rupture macroscopique d'un milieu poreux par homogénéisation non linéaireDetermination of the macroscopic strength criterion of a porous medium by nonlinear homogenization

A porous medium, which matrix is a perfectly plastic solid, is considered. This paper proposes a method to determine the macroscopic admissible stress states. The method is based on a homogenization technique which takes advantage of the equivalence, under certain conditions, between a problem of limit analysis and a ficticious nonlinear elastic problem. The particular case of a Drucker–Prager solid matrix is considered. The method provides an analytical expression for the complete macroscopic strength criterion. To cite this article: J.-F. Barthélémy, L. Dormieux, C. R. Mecanique 331 (2003).     

Modal analysis of a spinning disk in a dense fluid as a model for high head hydraulic turbines

In high head Francis turbines and pump-turbines in particular, Rotor Stator Interaction (RSI) is an unavoidable source of excitation that needs to be predicted accurately. Precise knowledge of turbine dynamic characteristics, notably the variation of the rotor natural frequencies with rotation speed and added mass of the surrounding water, is essential to assess potential resonance and resulting amplification of vibrations. In these machines, the disk-like structures of the runner crown and band as well as the head cover and bottom ring give rise to the emergence of diametrical modes and a mode split phenomenon for which no efficient prediction method exists to date. Fully coupled Fluid–Structure Interaction (FSI) methods are too computationally expensive; hence, we seek a simplified modeling tool for the design and the expected-life prediction of these turbines.We present the development of both an analytical modal analysis based on the assumed mode approach and potential flow theory, and a modal force Computational Fluid Dynamics (CFD) approach for rotating disks in dense fluid. Both methods accurately predict the natural frequency split as well as the natural frequency drift within 7.9% of the values measured experimentally. The analytical model explains how mode split and drift are respectively caused by linear and quadratic dependence of the added mass with relative circumferential velocity between flexural waves and fluid rotation.