| The granular material is a complex system consisting of a large number of randomly packed discrete solid particles interacting with each other. Its mechanical properties depend on the class of material, the shape, the size of the particles as well as particle arrangment. Granular materials are widespread in nature and in engineering practice, such as soil, rock, desert and drugs. The study of the mechanical behavior of granular materials has important significance in practce.The research contents of the present thesis include:We established a new model termed as parallel-column model for a rectangular sample of heterogeneous granular material composed of circular disks with random packing structure. The randomly packed granular material is assumed to be composed of a series of parallel particle columns. Within the framework of the proposed model, an expression for the structural stiffness coefficient of the rectangular granular sample is derived. The modified coefficient is introduced to take into account both the effect of the difference between the assumed parallel column microstructure and the heterogeneous microstructure over the granular sample with random particle packing and the effect of the inter-column interactions on the structural stiffness coefficient. The structural stiffness coefficient can be predicted using the proposed expression without microscopic analysis of the granular sample. To quantify the amount of grain crushing, the concept of relative breakage is adopted. The relative breakage parameter is then introduced into the proposed expression. Numerical results demonstrate the validity of the derived expression and show the effect of grain crushing on the structural stiffness coefficient of a granular sample.The expression for the structural stiffness coefficient of the randomly packed granular sample with consideration of the randomness and uncertainty of the material property of individual particles. The probability density function is introduced to characterize the randomness and uncertainty of the material property of individual particles. The agreement between the theoretical prediction of the stiffness coefficient of the granular sample given by the proposed expression and the numerical results obtained by the granular element method is very satisfactory. An analytical expression for the effective thermal conductivity of the randomly packed granular material is derived within the framework of the proposed model. The effective thermal conductivity is expressed in terms of particle size distribution, the compressive displacement, the structural size and thermal conductivity of individual particle. The agreement between theoretical predictions given by the expression and numerical results makes a compelling case that the major underlying physics of the heat transfer through the granular material is well reflected by the parallel-column model.The relationship between contact stiffness ratio and structural stiffness coefficient of the randomly packed granular material is investigated using the granular element method (GEM). Both regularly and randomly packed granular samples are studied with different contact force models and particle size distributions (PSDs) in numerical simulation using the GEM. Initial arrangements of particles in the granular samples are generated using the inwards packing and iterative growth methods. We demonstrate that as the degree of the randomness (DOR) of the granular sample increases from0to1, the relationship between the stiffness coefficient of the granular sample and the contact stiffness ratio evolves from a linear to a logarithmic-linear relationship.The present thesis develops the finite element procedure of gradient Cosserat continuum in the frame of the second-order computational homogenization for multiscale analysis of granular materials. The key issues are the appearance of strain gradients and how to attain Cl-continuity of the interpolation of displacement for a displacement-based finite element, i.e. both translational displacements and their first-order derivatives are required to be continuous across inter-element boundaries. It is very difficult to construct the finite element truly satisfying C1-continuity requirement in two or three dimension. To circumvent C1-continuity requirement, mixed finite element for gradient Cosserat continuum is developed and its formulation is derived on the basis of the weak form of the Hu-Washizu variational principle and the previous work for Cauchy continuum using Toupin-Mindlin gradient theory. Translational displacements, micro-rotations and displacement gradients with Lagrange multipliers are interpolated as independent variables. Only C0-continuity is required for the interpolation functions for the above4kinds of node degree of freedom The displacement-strain compatibility condition defined in gradient Cosserat continuum with the derivatives of the displacement gradients defined as independent variables in the mixed finite element is enforced in the weak form. Consequently, the micromechanically informed macroscopic stress-strain constitutive relation derived from the second-order computational homogenization is also satisfied in the weak form. The patch tests are performed to validate the present mixed finite element formulations for gradient Cosserat continuum in the frame of the second-order computational homogenization procedure, i.e. using micromechanically informed macroscopic constitutive relations. Numerical examples demonstrate the capability of the proposed mixed finite element procedure for the second-order computational homogenization using discrete particle assembly-gradient Cosserat continuum modeling in capturing the size effect of absolute size of the microstructure and the effect of high strain gradients for granular materials, in addition, in the simulation of the strain softening and localization phenomena while with no need to specify the macroscopic constitutive relation and material failure model. The micromechanical mechanisms of macroscopic failure of granular materials can also be revealed. |
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