During the macroscopic deformation of granular materials, which consist of an assembly of particles, the micromechanical structures change by forming new contacts or losing existing contacts. Among touching and non-touching particles in granular materials, touching particles contribute to macroscopic stress, which is given as the tensorial average of the contact forces between the particles. However, both touching and non-touching particles contribute to macroscopic strain, which is given by the tensorial average of the relative displacements between the particles. As non-touching particles lack contact force and contribute to no internal work, a constraint condition must be imposed on the macroscopic strain due to the non-touching particles; the work induced by the strain due to the non-touching particles must be zero. The strain that meets this constraint condition is called energy-less strain and it is studied further for applications to the macroscopic constitutive modeling of granular materials. The framework of the strain space multiple mechanism model is used to upscale the micromechanical structure of granular materials into the macroscopic constitutive modeling. Through this framework of study, the volumetric strain of the energy-less strain is identified as the dilative component of dilatancy in granular materials. The evolution of induced anisotropy, in terms of the fabric of the energy-less strain, is also identified.
Iai, S., & Ueda, K. (2016). Energy-less strain in granular materials – Micromechanical background and modeling. Soils and Foundations, 56(3), 391–398. https://doi.org/10.1016/j.sandf.2016.04.006