10.4 Stress_Model: Mises Viscoelastic Creep Model

MCREEP

Material_name = MCREEP

Material_set_number = mset , etc...

The constitutive equation is written as follows:

where E = isotropic elasticity tensor, = strain and = creep strain. The creep strain rate is given by:

where = effective or equivalent creep strain rate. In the model it is assumed that the bulk response is linear elastic and that the nonlinear creep response is restricted to the deviatoric part of the stress and strain. The effective creep strain is assumed to consist of contributions from primary (transient) creep, and secondary (steady-state) creep , as follows:

with:

if

if

and

where A, B, C, n, and Q are material parameters, T = absolute temperature (degrees Kelvin), and R = 1.987 cal/mole-K = universal gas constant. Values for the material parameters are given in Table 10.4.1.

Table 10.4.1

Material Primary Creep Secondary Creep

A B D n Q

(sec.^-1) (Pa^-4.9 /sec.) (cal/mole)

Halite 4.56 127. 5.39E-8 5.79E-36 4.9 12.0E+3

Argillaceous Halite 4.56 127. 5.39E-8 1.74E-35 4.9 12.0E+3

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

Coefficient_A real [4.56] Material parameter A

Coefficient_B real [127.] Material parameter B

Coefficient_E real [5.39E-8] Material parameter

Coefficient_D real [5.79E-36] Material parameter D

Coefficient_n real [4.9] Power exponent n

Coefficient_Q real [12.E+3] Material parameter Q

(cont'd)

(cont’d)

Note Variable Name Type Default Description

Reference_temperature real [273.15] Reference Temperature T₀

(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 ()

(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

(3) Ref_fluid_pressure real [0.0] Reference pore-fluid pressure

(3) Pressure_load_time integer [0] Pore-fluid pressure load time function

• List Read Method

Material data must follow in the form:
< m, IHyper(m), G(m), B(m), (m), (m), (m), (m), Pf(m) >

< A(m), B(m), E(m), D(m), n(m), Q(m), (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 . .