This work is devoted to the generalizations of Mohr-Coulomb approach to the modeling of granular materials, based on hypoelastic and hypoplastic theories. The formulations and analyses of such models are given from a phenomenological-thermodynamic point of view, in the context of Müller-Liu entropy principle. First, the basis constitutive assumptions are introduced and discussed. In particular, the authors consider the form of evolution relation for a second-order, symmetric-tensor-valued spatial internal variable, accounting for internal friction and associated with the effective contact stress in granular materials, together with the assumption of material isotropy. Then the corresponding form of entropy inequality is formulated, based on Müller-Liu entropy principle. The exploitation of this inequality yields direct restrictions on the coefficients of the so-called potential and flux on-forms defined on the manifold of independent constitutive variables. Further, considering the associated integrability conditions, the authors derive restrictions on the constitutive form of entropy fluxes and energy Lagrange multipliers. The exploitation of entropy principle is completed by restrictions obtained from the residual inequality in the context of thermodynamic equilibrium. Finally, two special cases, namely the hypoelastic-like and hypoplastic-like evolution relations for the internal variable accounting for internal friction are investigated. It is shown that for the hypoelastic-type models, a true equilibrium inelastic Cauchy stress exists. At the same time, such a stress does not exist for the hypoplastic model due to its rate-independence and incremental non-linearity. With the help of a slight generalization of the thermodynamic equilibrium (i.e., to thermodynamic ``quasi-equilibrium''), using the so-called non-standard analysis, the authors introduce Cauchy stress for the hypoplastic model. The obtained results are compared with previous works of other authors.