Elastic stress transfer model and homogenized constitutive equation for the multi-phase geomaterials

Abstract

Multi-phase geomaterials can be classified as the particulate composites composed of finer matrix and dispersed inclusions. With the extremely nonuniform stress and strain field, prediction of the overall mechanical response from the known mechanical properties and mixed proportion of constituents is a challenging task for multi-phase geomaterials. In this paper, using a concentric composite cylinder as the equivalent representative volume element (RVE), the analytical solutions of stress transfer model are derived from the modified shear-lag analysis. Through the mechanical homogenization of internal stress/strain field, a constitutive equation has been established in the elastic regime, containing a closed-form solution (S-L method) for prediction of effective Young's modulus (EHom). By the comparison with classical models, numerical simulations and experimental results, the homogenized constitutive equation (EHom) has been validated. Meanwhile, parametric studies of proposed solutions have been conducted to discuss the effect of meso-mechanical variables (e.g., mechanical contrast and volume proportion of constituents) on the stress transfer mechanism and the overall mechanical response, providing the useful insights and explanations to previous studies.