10.6 Stress_Model: Drucker-Prager Elasto-(Visco-)Plastic Model

DRUCKER_PRAGER

Material_name = DRUCKER_PRAGER

Material_set_number = mset , etc...

The yield function is of the following type:

where

 and c are material constants, = effective (Kirchhoff) stress. The Drucker-Prager cone which is internally tangential to the Mohr-Coulomb yield surface is obtained by setting:

where C_MC = Mohr-Coulomb cohesion, = Mohr-Coulomb friction angle. The external cone is obtained by setting:

If an associative flow rule is used. Otherwise a non-associative flow rule is used. The following hyperelastic stored energy function with uncoupled volumetric and deviatoric parts is employed:

where

Note Variable Name Type Default Description

• Keywords Read Method

Material_set_number integer [1] Material set number Numat

(1) Hyperelastic_case integer [0] Hyperelastic free energy function:

Mass_density real [0.0] Mass density

Shear_modulus real [0.0] Shear modulus G

Bulk_modulus real [0.0] Bulk modulus B

Activation_time real [0.0] Time at which nonlinearities are activated.

Friction_angle real [0.0] Friction angle > 0.0

Cohesion real [0.0] Cohesive coefficient c

Dilation_angle real [0.0] Dilation angle 0.0

Internal_cone list [on] Internal cone option

on / off

Tension_cutoff list [off] Tension cutoff options

on / off

Relaxation_time real [0.0] Relaxation time constant 0.0

0.0, Elastoplastic

> 0.0, Elastoviscoplastic

Variable_cohesion integer [0] Variable cohesion load time function number

Variable_friction integer [0] Variable friction angle load time function

number

(2) Initial_stress

initial_stress_11 real [0.0] Component 11 ()

initial_stress_22 real [0.0] Component 22 ()

initial_stress_33 real [0.0] Component 33 ()

initial_stress_12 real [0.0] Component 12 ()

initial_stress_23 real [0.0] Component 23 ()

initial_stress_31 real [0.0] Component 31 ()

(cont’d)

(cont'd)

Note Variable Name Type Default Description

(3) Solid_mass_density real [0.0] Mass density (solid phase)

(3) Fluid_mass_density real [0.0] Mass density (fluid phase)

(3) Fluid_bulk_modulus real [0.0] Fluid bulk modulus

(3) Porosity real [0.0] Porosity

• List Read Method

Material data must follow in the form:

< m, IHyper(m), G(m), B(m), (m), (m), (m), (m), Pf(m) >

< (m), c(m), (m), (m), ltime_coh(m), ltime_phi(m) >

< (Stres(i, m), i = 1, 6) >

< terminate with a blank record >.

Notes/

(1) Only applicable to finite deformation case (see Section 9.2.1).

(2) Tensile stresses are positive.

(3) Only applicable to porous media models.

Notes . .