Internal Structure Quantification for Granular Constitutive Modeling

The importance of internal structure on the stress-strain behavior of granular materials has been widely recognized. How to define the fabric tensor and use it in constitutive modeling, however, remains an open question. The definition of fabric tensor requires (1) identifying the key aspects of structure information, and (2) quantifying their impact on material strength and deformation. This paper addresses these issues by applying the homogenization theory to interpret the multiscale data obtained from the discrete element simulations. Numerical experiments have been carried out to test granular materials with different particle friction coefficients. More frictional particles tend to form fewer but larger void cells, leading to a larger sample void ratio. Upon shearing, they form more significant structure anisotropy and support higher force anisotropy, resulting in higher friction angle. Material strength and deformation have been explored on the local scale with the particle packing described by the void cell system. Three groups of fabric tensor are discussed herein. The first group is based on the contact vectors, which are the geometrical links between contact forces and material stress. Their relationship with material strength has been quantified by the Stress-Force-Fabric relationship. The second group is based on the statistics of individual void cell characteristics. Material dilatancy has been interpreted by tracing the void cell statistics during shearing. The last group is based on the void vectors, for their direct presence in the microstructural strain definition, including those based on the void vector probability density and mean void vector. Correlations among various fabric quantifications have been explored. The mean void vector length and the mean void cell area are parameters quantifying the internal structure size and strongly correlated with each other. Anisotropy indices defined based on contact normal density, void vector density, void vector length, and void cell orientation are found to be effective in characterizing loading-induced anisotropy. They are also closely correlated. An in-depth investigation on structural topology may help establish the correlation among different fabric descriptors and unify the fabric-tensor definition. Deformation bands have been observed to continuously form, develop, and disappear over a length scale of several tens of particle diameters. Its relation to and impact on material deformation is an area of future investigation.