MATSUOKA
Material_name = MATSUOKA
Material_set_number = mset , etc...
The yield function is of the following type :
f = cyJ3 - (cy - 3)(p - at)J2 + (cy - 9)(p - at)3 = 0
where
s = 
- p
p = tr()/3 J2 = tr(s2)/2 J3
= tr(s3)/3 = det(s)
cy and at are material constants. The Matsuoka cone which is closest to the Mohr-Coulomb yield surface is obtained by setting:
cy = (9 - sin
) / (1 - sin) at = c tan
where
c = Mohr-Coulomb cohesion, = Mohr-Coulomb friction angle. If the dilation angle 
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
References / Bibliography
1. Matsuoka, H. and T. Nakai, "Relationship Among Tresca, Mises, Mohr-Coulomb and Matsuoka-Nakai Failure Criteria," Soils and Foundations, 5, No. 4, (1985), 123–128.
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:
Tension_cutoff list [off] Tension cutoff options:
on / off
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
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 (
)
(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
(cont'd)
(cont'd)
Note Variable Name Type Default Description
• 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 . .