Hydrostatic and shear behavior of frictionless granular assemblies under different deformation conditions

摘要

Stress- and structure-anisotropy (bulk) responses to various deformation modes are studied for dense packings of linearly elastic, frictionless, polydisperse spheres in the (periodic) triaxial box element test configuration. The major goal is to formulate a guideline for the procedure of how to calibrate a theoretical model with discrete particle simulations of selected element tests and then to predict another element test with the calibrated model (parameters).ud 　Only the simplest possible particulate model material is chosen as the basic reference example for all future studies that aim at the quantitative modeling of more realistic frictional, cohesive powders. Seemingly unrealistic materials are used to exclude effects that are due to contact non-linearity, friction, and/or non-sphericity. This allows us to unravel the peculiar interplay of stress, strain, and microstructure, i.e. fabric.ud 　Different elementary modes of deformation are isotropic, deviatoric (volume-conserving), and their superposition, e.g. a uniaxial compression test. Other ring-shear or stress-controlled (e.g. isobaric) element tests are referred to, but are not studied here. The deformation modes used in this study are especially suited for the bi- and triaxial box element test set-up and provide the foundations for understanding and predicting powder flow in many other experimental devices. The qualitative phenomenology presented here is expected to be valid, even clearer and magnified, in the presence of non-linear contact models, friction, non-spherical particles and, possibly, even for strong attractive/ adhesive forces.ud 　The scalar (volumetric, isotropic) bulk properties, the coordination number and the hydrostatic pressure scale qualitatively differently with isotropic strain. Otherwise, they behave in a very similar fashion irrespective of the deformation path applied. The deviatoric stress response (i.e. stressanisotropy), besides its proportionality to the deviatoric strain, is cross-coupled to the isotropic mode of deformation via the structural anisotropy; likewise, the evolution of pressure is coupled via the structural anisotropy to the deviatoric strain, leading to dilatancy/compactancy. Isotropic/uniaxial over-compression or pure shear respectively slightly increase or reduce the jamming volume fraction below which the packing loses mechanical stability. This observation suggests a necessary generalization of the concept of the jamming volume fraction from a single value to a “wide range” of values as a consequence of the deformation history of the granular material, as “stored/memorized” in the structural anisotropy.ud 　The constitutive model with incremental evolution equations for stress and structural anisotropy takes this into account. Its material parameters are extracted from discrete element method (DEM) simulations of isotropic and deviatoric (pure shear) modes as volume fraction dependent quantities. Based on this calibration, the theory is able to predict qualitatively (and to some extent also quantitatively) both the stress and fabric evolution in another test, namely the uniaxial, mixed mode during compression. This work is in the spirit of the PARDEM project funded by the European Union