5.1.2 Mohr-Coulomb or Drucker-Prager

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...ace{14.6mm}{[}\>\texttt{HARDEN}\>\texttt{STRAIN}\,{]} \end{tabbing} \end{figure}$

YIELD

specifies the criterion to be used: MOHRCO for Mohr-Coulomb [§17.1.3] or DRUCKE for Drucker-Prager [§17.1.4].

YLDVAL

specifies the yield surface: ch is the cohesion c , sph is sin $\phi$ of friction angle $\phi$ and sps is sin $\psi$ of dilatancy angle $\psi$ . ( $\psi$ $\leq$ $\phi$ )Associated plasticity if $\psi$ = $\phi$ , nonassociated plasticity if $\psi$ < $\phi$ .

HARDIA

is the hardening diagram: ch1 to chn are the mobilized cohesions c , (n $\leq$ 25 )k1 to kn are the corresponding hardening parameters $\kappa$ .

FRCDIA

specifies a hardening diagram for the friction angle. The apex of the yield criterion will remain on its place. Values sph1 to sphn are the sin $\phi$ of the mobilized friction angles $\phi$ and k1 to kn (n $\leq$ 25 )are the corresponding hardening parameters $\kappa$ .

DILDIA

specifies plastic dilatancy as a function of the hardening parameter. Values sps1 to spsn (n $\leq$ 25 )are the sin $\psi$ of the mobilized dilatancy angles $\psi$ and k1 to kn are the corresponding hardening parameters $\kappa$ .

HARDEN

specifies the hardening hypothesis: STRAIN for strain hardening, which is the only one available. [STRAIN]

and the dilatancy angle $\psi$ are considered to remain constant, i.e., no ambient influence on these parameters. The values of $\phi$ and $\psi$ must be specified with record YLDVAL as described in the previous section^5.1.

No hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...extit{mvz}}$_{r}\,$ \texttt{\textit{chz}}$_{r}\,$ \end{tabbing} \end{figure}$

Values cha to chz are the cohesion c_a to c_z , respectively valid for the corresponding z (z $\leq$ 30 ) ambient values.

TEMYLD: specifies temperature influence, tea to tez are temperatures T .
CONYLD: specifies concentration influence, coa to coz are concentrations C .
MATYLD: specifies maturity influence, mva to mvz are maturity variables M .

(file.dat)

'MATERI'
  1   YIELD     MOHRCO
      CONYLD    0.0  500.0
                1.0  400.0

Hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...2}}$_{r}\,$ \ldots \texttt{\textit{chzn}}$_{r}\,$ \end{tabbing} \end{figure}$

Ambient dependent hardening needs the specification of hardening diagrams for the z (z $\leq$ 30 ) ambient values.

KAPPA k1 ...kn: (n $\leq$ 30 )are the equivalent plastic strains $\kappa$ for which points in the diagrams are specified.
cha1 ...chan: are the cohesions c , valid at ambient value __a for the specified $\kappa$ 's. Values chb1 to chbn are valid at ambient value __b etc.

TEMYLD: specifies temperature influence, tea ...tez are temperatures T .
CONYLD: specifies concentration influence, coa ...coz are concentrations C .
MATYLD: specifies maturity influence, mva ...mvz are maturity variables M .

(file.dat)

'MATERI'
  1   YIELD    MOHRCO
      KAPPA             0.00   0.01   1.00
      TEMYLD   -100.0  500.0  700.0  700.0
                100.0  500.0  700.0  700.0
                500.0  400.0  450.0  450.0
                700.0  300.0  300.0  300.0

5.1.2.2 User-supplied

DIANA offers the user-supplied subroutine mechanism for cases where the hardening or the ambient influence on the cohesion for the Mohr-Coulomb or Drucker-Prager criterion cannot be input as described. In this case the criterion name as indicated in the previous sections must be specified together with the data records in this section. The cohesion can be a function of equivalent plastic strain, temperature, concentration, maturity and time.

Hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...{USRPAR}\>\texttt{\textit{usrpar}}$_{r\ldots}\,${]} \end{tabbing} \end{figure}$

YIELD: specifies the criterion to be used: MOHRCO for Mohr-Coulomb [§17.1.3] or DRUCKE for Drucker-Prager [§17.1.4].
SINPHI: sphi specifies sin $\phi$ , the sine of the friction angle $\phi$ .
SINPSI: spsi specifies sin $\psi$ , the sine of the dilatancy angle $\psi$ . ( $\psi$ $\leq$ $\phi$ )If you don't specify sin $\psi$ then DIANA assumes associated plasticity. [ $\psi$ = $\phi$ ]
COHCRV: USRCRV specifies that the cohesion is determined via the user-supplied subroutine USRCRV [§11.3.1].
USRPAR: usrpar are the parameters of the hardening curve.

DIANA passes the following information to subroutine USRCRV: the character string 'COHCRV' via argument parnam and parameters usrpar via argument usrpar.

(file.dat)

'MATERI'
  1   YIELD    MOHRCO
      SINPHI   0.5
      COHCRV   USRCRV

5.1.2.3 Position Dependency

For some materials the cohesion c may depend on the position of the material in space. A typical example is soil where c may vary with the depth in the soil layer. To model such a dependency, DIANA can apply gradient characteristics on the Mohr-Coulomb plasticity model without temperature influence.

DIANA can only handle position dependency for numerically integrated plane stress, plane strain, axisymmetric and solid elements. Position dependency cannot be applied in combination with a user-supplied subroutine.

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...t{grchy}}$_{r}\,$ \texttt{\textit{grchz}}$_{r}\,$ \end{tabbing} \end{figure}$

YIELD: specifies the criterion to be used: MOHRCO for Mohr-Coulomb which is the only one available in combination with gradient characteristics.
YLDVAL: specifies the yield surface: chref is the reference cohesion c_ref , sph is sin $\phi$ of friction angle $\phi$ and sps is sin $\psi$ of dilatancy angle $\psi$ . ( $\psi$ $\leq$ $\phi$ )
REFPOS: specifies the reference position where xref, yref, and zref respectively are the coordinates ( X_ref, Y_ref, Z_ref ) of the reference point R for which c = c_ref .
COHGRD: specifies the gradient of the cohesion in the global XYZ directions: $\partial$ c/ $\partial$ X = grx , $\partial$ c/ $\partial$ Y = gry , $\partial$ c/ $\partial$ Z = grz .

DIANA will calculate the cohesion for each element integration point via linear interpolation:

c(X, Y, Z) = c_ref + (X - X_ref) $\displaystyle {\frac{{ \partial c }}{{ \partial X }}}$ + (Y - Y_ref) $\displaystyle {\frac{{ \partial c }}{{ \partial Y }}}$ + (Z - Z_ref) $\displaystyle {\frac{{ \partial c }}{{ \partial Z }}}$

(5.3)

where c_ref is the reference cohesion whose value is supposed to be specified in the hardening diagram via input item HARDIA [§5.1.2]. The other input data FRCDIA, DILDIA and HARDEN is analogous to the input for constant properties.

Next: 5.1.3 Rankine Principal Stress Up: 5.1 Isotropic Plasticity Previous: 5.1.1 Tresca or Von Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.