Continuum Modeling Using Granular Micromechanics Approach: Method Development and Applications

This work presents a constitutive modeling approach for the behavior of granular materials. In the granular micromechanics approach presented here, the material point is assumed to be composed of grains interacting with their neighbors through different inter-granular mechanisms that represent material’s macroscopic behavior. The present work focuses on (i) developing the method for modeling more complicated material systems as well as more complicated loading scenarios and (ii) applications of the method for modeling various granular materials and granular assemblies. A damage-plasticity model for modeling cementitious and rock-like materials is developed, calibrated, and verified in a thermo-mechanically consistent manner. Grain-pair interactions in normal tension, normal compression, and tangential directions have been defined in a manner that is consistent with the material’s macroscopic behavior. The resulting model is able to predict, among other interesting issues, the effects of loading induced anisotropy. Material’s response to loading will depend on the loading history of grain-pair interactions in different directions. Thus the model predicts load-path dependent failure. Due to the inadequacies of first gradient continuum theories in predicting phenomena such as shear band width, wave dispersion, and frequency band-gap, the presented method is enhanced by incorporation of non-classical terms in the kinematic analysis. A complete micromorphic theory is presented by incorporating additional terms such as fluctuations, second gradient terms, and spin fields. Relative deformation of grain-pairs is calculated based on the enhanced kinematic analysis. The resulting theory incorporates the deformation and forces in grain-pair interactions due to different kinematic measures into the macroscopic behavior. As a result, non-classical phenomena such as wave dispersion and frequency band-gaps can be predicted. Using the grain-scale analysis, a practical approach for calibrating model parameters corresponding to micromorphic continua is also presented that can be used for any given material system or grain assembly