Exploring emergence of critical state and one-dimensional compression through a granular micromechanics model

The mechanical behavior of granular materials, explored by frictional and collisional mechanisms, is elucidated with the stress-strain relations thanks to the properly modified for damage and plasticity phenomena under complex loading paths. In this thesis, a Granular Micromechanics Approach (GMA) based continuum model offers a fresh perspective to investigate the classical loading scenarios such the emergence of a critical state and one-dimensional uniaxial compression. Moreover, a continuum model is established based on elastic energy and dissipation potential definitions with regard to the grain-pair interactions in different orientations. A hemi-variational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain-pair, respectively, with a decrease in stiffness and irreversible deformation. As a consequence, the Karush-Kuhn-Tucker (KKT)-type conditions are derived, which give the evolution equations for the irreversible phenomena. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain-pair to the continuum description. The mechanical response of granular materials is characterized by: i) a critical state, in which deformation occurs without change of material volume or stresses when subjected to large shear deformation; and ii) one-dimensional uniaxial compression, where the material is loaded with a monotonically increasing vertical compressive displacement until a specific threshold is reached. The mechanical behavior of these concepts is shown to emerge as grain-pair related damage and plastic evolution, interacting in a competitive/collaborative manner during the imposed loading path. Uniaxial or one-dimensional compression is widely used in granular material processing to produce granular compacts and is a key experimental method for evaluating the compressibility of granular materials. To describe the stiffening behavior that elasto-frictional granular materials exhibit in confined compression, the elastic energy functional and dissipation potential were modified from previous versions of GMA-based models. The modified model, derived in the framework of geometrically nonlinear deformations, was then applied to replicate experimentally measured one-dimensional compression behavior of granular materials undergoing large compression. The results reveal nearly universal scaling with respect to the model parameters for predicting the behavior of granular materials composed of different particle types or initial density. In the second work of one-dimensional compression, the elastic energy of a generic grain-pair direction of a GMA is reformulated consisting of a complete quadratic and quartic (duffing) dependencies on normal and tangential relative displacements to capture various nuances of material nonlinearity. It is shown that the coupling of this nonlinear elastic and the damage-plastic behavior yields an apparent molecular-type, such as Lennard-Jones type, potential for the granular system. Classical behavior of lateral earth pressure coefficient, the ratio of lateral to axial stress, is predicted by the model. The constitutive model is conducted in a stepwise manner to identify the evolution of damage and plastic irreversible variables related frictional grain-pair mechanism. In this thesis, the emergence of critical state and one-dimensional uniaxial compression are investigated for the first time through the collaboration of coupled damage and plastic mechanics within a granular micromechanics based continuum description.