Theory of consolidating granular media

The general theory of granular media with particles able to join (consolidate) is developed (2001) [1, 2]. The particles possess translational and rotational degrees of freedom. For isotropic material with small displacements and isothermal strains the theory of consolidating granular media is developed in a closed form [1].

It is shown that the assumption that the tensor of viscous stresses depends on velocity, leads either to failure of dissipative inequality, or to failure of hyperbolicity [1]. Hence this assumption is unacceptable. Instead of the tensor of viscous stresses, which is frequently used in literature, the antisymmetric stress tensor is introduced [1]. For this tensor the Coulomb friction law is used. For the couple stress tensor the viscous friction law is used, and this tensor is assumed to be antisymmetric.

  1. Zhilin P.A. Basic equations of the theory of non-elastic media // Proc. of the XXVIII Summer School “Actual Problems in Mechanics”. St. Petersburg. 2001. P. 14-58. (In Russian.)
  2. Zhilin P.A. Phase Transitions and General Theory of Elasto-Plastic Bodies // Proceedings of XXIX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia, 2002. P. 36-48.