Micromechanics-inspired granular thermodynamics: A constitutive model for multidirectional cyclic shearing

Abstract

A new micromechanics-inspired thermodynamic constitutive model is developed for fluid-saturated granular materials. The model development begins with the conceptual assumption that a granular material, when subjected to an external load, is supported by networks of microscopic force chains, including strong and weak force networks. The model also considers the heterogeneous nature of the fabrics in these force networks and describes these micro-level fabrics as a set of distributed fabric tensors. Using non-equilibrium thermodynamic principles, the micro-level behaviors in the strong and weak force networks are homogenized into two macro-level spaces: fabric-transformed space and real space. The model employs fabric-dependent granular hyperelasticity with free and residual elastic potentials, which leads to a fabric-dependent yielding criterion evaluated from the instability of micro-level elasticity. The granular plastic relationships are thermodynamically derived in combination with the concepts of fluidization index and granular temperature. Consequently, the thermodynamic transformations of stresses, strains, and plastic dissipative flows in the two macro-level spaces are derived. The model developed is capable of simulating granular fluidization (i.e., cyclic liquefaction). Its performance is validated by simulating undrained cyclic tests of Monterey No. 0/30 sand under different types of multidirectional non-proportional cyclic paths. The analysis of the developments in yielding and various internal factors of this model provides valuable insights into the mechanisms governing the critical state and non-coaxial cyclic behavior of granular materials.