A constitutive theory is developed for granular material undergoing arbitrarily large deformations. A three-dimensional discrete element model (DEM) was developed to simulate granular material. The computational efficiency of the discrete element model was improved to allow for modeling of large particle systems. The need for large particle simulations was in order to develop an ability to model laboratory experiments on a one-to-one basis so that the discrete element model could be evaluated against real soils. A comparison was made between laboratory experiments involving very large discontinuous deformations in sand and numerical simulations, using a large-scale DEM computation. The magnitude of the simulation provided a unique opportunity to assess the validity of the DEM, based on experimental results. The agreement between the experimental and simulated particle motions in the plowing experiment indicates that many details not captured by the simplistic particle interaction model may not be relevant in statistically large assemblies.; Once it was established that the discrete element method provided a reasonable model for real granular material, an averaging scheme to convert properties local to the particles (e.g. mass, momentum) into continuum attributes (e.g. density, velocity gradients) was developed. From this averaging scheme a new constitutive law was developed to model large deformation of granular material. It is concluded that without a micro-mechanical approach based on physical measurements, a satisfactory theory would be difficult to develop. Measurement at the micro-mechanical level is, of course, not possible with real materials. The Discrete Element Method (DEM) is used to simulate a particulate medium from which micro-mechanical quantities can be obtained. The analysis begins with consideration of a smoothing of the DEM quantities, which amounts to application of a weighted residual approximation of the difference equations governing the DEM simulations. The analysis carries with it relationships needed to create a coarsened particulate system as a numerical approximation to the granular media. The momentum balance equation of the smoothed continuum is non-local but reduces to the familiar differential form of classical local continuum mechanics in the asymptotic limit when particle size is small relative to the domain size. Similarly, a deformation gradient can be defined that is a thermodynamic conjugate to the (smoothed) Cauchy stress. The stress is obtained as the mean of the outer product of inter-particle force and contact vectors by application of the virtual work principle. The evolution of contact properties is not readily determined from averaged particle movements because of non-affine components of particle interaction. However, the smoothing process eliminates spatial detail and only the statistical descriptions of particle interactions are needed to evaluate the equations of motion. The key to a continuum theory for granular media, therefore, is to relate the statistics of particle interactions to the kinematics of the smoothed system.
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