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Hypoplasticity + Intergranular Strain (Hypo+IGS):

*Mechanical = Hypoplasticity   
phi [rad], nu [-], h_s [F/A], n [-], e_d0 [-], e_c0 [-], f_ei0 [-], alpha [-] 
beta [-], m_T [-], m_R [-], R [-], beta_R [-], chi [-], K^w [F/A]

The material parameters of the hypoplastic model with intergranular strain are given in the following.

  • \(\varphi_c\) [rad] is the critical friction angle and has to be provided in radian.
  • \(h_s\) [F/A] and \(n\) [-] describe the decrease of the maximum void ratio \(e_i\) with increasing pressure during isotropic compression. This parameter has no unit.
  • The void ratios \(e_{d0}\) [-] and \(e_{c0}\) [-] correspond to the densest and the critical state. The parameter \(f_{ei0}\) is used to calculate the void ratio at the loosest state \(e_{i0}=f_{ei0}\cdot e_{c0}\) at pressure \(p\) = 0 F/A. Usually \(f_{ei0}=1.15\) is used. These parameters have no unit.
  • The material constant \(\alpha\) describes the influence of density on the peak friction angle. This parameter has no unit.
  • \(\beta\) mainly influences the stiffness of dense soil skeletons. This parameter has no unit.
  • \(R\) is the radius of intergranular strain. This parameter has no unit.
  • \(\beta_R\) and \(\chi\) describe the evolution of the intergranular strain tensor along a strain path, i.e. the reduction of the shear modulus with increasing shear strain. These parameters have no unit.
  • \(m_R\) and \(m_T\) govern the increase of the stiffness due to changes of the direction of the strain path by \(180^\circ\) (\(m_R\)) or \(90^\circ\) (\(m_T\)), respectively. These parameters have no unit. An often applied assumption is: \(m_T = m_R/2\).
  • \(\bar{K}^w\) is the bulk modulus of pore water for locally undrained simulations (and only for those). The parameter is not mandatory and zero per default.

State variables

In addition to the (effective) stress, the hypoplastic constitutive model takes additional state variables. Performing simulations with this model requires the prescription of those. The following state variables are contained in the model:

  • Void ratio: \(e\), void_ratio. The prescription of the void ratio is mandatory, if the initialization is omitted or wrong values are prescribed the simulation will abort.
  • Intergranular strain: \(R_{ij}\), int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13. Only in combination with the intergranular strain extension. Prescribing \(R_0\) is not mandatory, if omitted, \(R_{ij}\) is assumed. \(R_{ii} = R_0 / \sqrt{3}\) corresponds to an isotropically consolidated state.

The state variables can be initialized in two different ways:

  • Using the *Initial conditions, type = state variables command in the input file, e.g. 
    *Initial conditions, type = state variables  
element_set_name, void_ratio, <value>  
`` 
element_set_name, int_strain11, <value>  
element_set_name, int_strain22, <value>  
element_set_name, int_strain33, <value>
  • Using the interface for user-defined initial state variables. In this approach, the vector holding the state variables is filled directly in a fortran subroutine as described in Section: User defined state variables. The position of the state variables in the associated vector are as follows: statev(1) = \(e\), statev(2) = \(R_{11}\), statev(3) = \(R_{22}\), statev(4) = \(R_{33}\), statev(5) = \(R_{12}\), statev(6) = \(R_{23}\), statev(7) = \(R_{13}\)

Additional output variables

The following additional output variables are available in the *Output command:

  • Void ratio: void_ratio
  • Intergranular strain: int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13.
  • Stress projection: proj. Flag that indicates if the stress correction is active (see Theory Manual). iproj takes the value of 0 if the stress projection is inactive.