Probability density functions of contact forces for cohesionless frictional granular materials |
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| Institution: | 1. Department of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands;2. Department of Civil Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;1. National Fusion Research Institute, Daejeon, Republic of Korea;2. Korea Atomic Energy Research Institute, Daejeon, Republic of Korea;1. Key Laboratory of Optoelectronic Devices and Systems, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China;2. Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, China;3. School of Foreign Studies, Xi’an Jiaotong University, Xi’an, 710049, China;4. Shaanxi Key Lab. of Advanced Nuclear Energy and Technology, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, 710049, China;5. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China;6. China Nuclear Power Engineering Co., Ltd, Shenzhen 518124, China;1. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China;2. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China;3. University of Science and Technology of China, Hefei, Anhui 230027, China;1. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China;2. University of Science and Technology of China, Hefei, Anhui 230027, China;3. North China Electric Power University, Beijing 102206, China;1. Mechanical and Aerospace Engineering Department, University of California, Los Angeles 420 Westwood Plaza, Los Angeles, CA, 90095-1597, USA;2. Korean Atomic Energy Institute, Daejeon, Republic of Korea;3. National Fusion Research Institute, Daejeon, Republic of Korea;1. Department of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands;2. Univ. Grenoble Alpes, Grenoble INP, CNRS, 3SR, F-38000 Grenoble, France;3. Institut für Geotechnik, Technische Universität Dresden, D-01062 Dresden, Germany |
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| Abstract: | A theory is developed for the probability density functions of contact forces for cohesionless, frictional granular materials in quasi-static equilibrium. This theory is based on a maximum information entropy principle, with an expression for information entropy that is appropriate for granular materials. Entropy is maximized under the constraints of a prescribed stress and that the normal component of the contact force is compressive and that the tangential component of the contact force is limited by Coulomb friction. The theory results in a dependence of the probability density function for the tangential contact forces on the friction coefficient. The theoretical predictions are compared with results from discrete element simulations on isotropic, two-dimensional assemblies under hydrostatic stress. Good qualitative agreement is found for means and standard deviations of contact forces and the shape of the probability density functions, while the quantitative agreement is fairly good. Discrepancies between theory and simulations, such as the difference in shape of the probability density function for the normal force and the observed dependence on elastic properties of the exponential decay rate of tangential forces, are attributed to the fact that the method does not take into account any kinematics, which are essential in relation to elastic effects. |
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