Abstract
1.1.Introduction.................................. 11 1.2.Descriptionofgranulartexture ....................... 13 1.2.1.Particleconnectivity .......................... 13 1.2.2. Contact network anisotropy: fabric tensors . . . . . . . . . . . . . 15 1.2.2.1.Generalcase ........................... 15 1.2.2.2.Caseof2Ddata ......................... 17 1.2.2.3.Caseof3Ddata ......................... 21 1.2.3.Branchvectors ............................. 24 1.2.4.Evolutionofgranulartexture ..................... 26 1.2.5.Spacepartition:tessellation...................... 28 1.2.5.1.Voronoicells ........................... 28 1.2.5.2.Dirichletcells........................... 28 1.2.5.3.Generalcase ........................... 29 1.2.5.4.Neighborhoodsandlocalvoidratios . . . . . . . . . . . . . . 29 1.3.Granularkinematics ............................. 31 1.3.1.Particledisplacementsandrotations . . . . . . . . . . . . . . . . . 31 1.3.2.Rollingvs.sliding ........................... 33 1.3.3.Fluctuatingdisplacementfields.................... 34 1.3.3.1.Uniformstrainandfluctuations. . . . . . . . . . . . . . . . . 34 1.3.3.2.Probabilitydensities....................... 37 1.3.3.3.Spatialcorrelations........................ 37 1.3.3.4.Granulence ............................ 38 1.3.4.Localandglobalstrains ........................ 39 1.3.4.1.Particle-scalestrain ....................... 39 1.3.4.2.Strainlocalization ........................ 40 1.4.ForceTransmission.............................. 43 9 10 Micromechanics 1.4.1.Probabilitydensityfunctions ..................... 43 1.4.2.Bimodalcharacterofstresstransmission . . . . . . . . . . . . . . 50 1.4.3.Forceanisotropy ............................ 54 1.5.Conclusion .................................. 56 1.6.Bibliography ................................. 57