Product: ABAQUS/Standard
Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, 
=0.3
Uniaxial tension, C3D8 elements.
Uniaxial tension, CPS4 elements.
Uniaxial tension, T3D2 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
Cyclic loading, T3D2 elements.
Linear perturbation steps containing *LOAD CASE, uniaxial tension, C3D8 elements.
Uniaxial tension with nonzero initial condition for 
, C3D8 elements.
Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
Cyclic loading, T3D2 elements.
Uniaxial tension with nonzero initial condition for 
, load control, T3D2 elements.
Cyclic loading, T3D2 elements.
Uniaxial tension with nonzero initial condition for , load control, T3D2 elements.
Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
Plasticity
Initial yield stress: 
=200.0
Isotropic hardening parameter, 
=2000.
Isotropic hardening parameter, b=0.25
Kinematic hardening parameter, C=2.222 × 104
Kinematic hardening parameter, 
=34.65
Uniaxial tension with temperature and field variable dependence, displacement control, SAX1 elements.
Uniaxial tension, tabulated data, load control, B21 elements.
Cyclic loading, no isotropic hardening, displacement control, T3D2 elements.
Simple shear including perturbation step, CPS4 elements.
Uniaxial tension, load control, C3D8 elements.
Uniaxial tension, nonzero initial conditions for , , and 
; displacement control; M3D4 elements with rebar.
Uniaxial tension with orientation and nonzero initial conditions for and , displacement control, CPE4 elements.
Uniaxial tension with temperature and field variable dependence, displacement control, SAX1 elements.
Uniaxial tension, tabulated data, load control, B21 elements.
Cyclic loading, no isotropic hardening, displacement control, T3D2 elements.
Simple shear including perturbation step, CPS4R elements.
Uniaxial tension, load control, C3D8R elements.
Uniaxial tension, nonzero initial conditions for , , and ; displacement control; M3D4R elements with rebar.
Uniaxial tension with orientation and nonzero initial conditions for and , displacement control, CPE4R elements.
Elasticity
Young's modulus, E=30.0E6
Poisson's ratio, =0.3
Plasticity
Other properties
Density, 
=1000.0
Specific heat, c=0.4
Inelastic heat fraction = 0.5
(The units are not important.)
Uniaxial tension, C3D8 elements.
Uniaxial tension, T3D2 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
Triaxial, C3D8 elements.
Uniaxial tension, C3D8 elements.
Multiaxial, C3D8 elements.
Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
Plasticity
(The units are not important.)
Uniaxial tension in direction 1, C3D8 elements.
Uniaxial tension in direction 2, C3D8 elements.
Uniaxial tension in direction 3, C3D8 elements.
Linear perturbation steps containing *LOAD CASE, uniaxial tension in direction 1, C3D8 elements.
Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
Plasticity
Yield stress, 
=200.0
Exponent, n=21.315
Yield offset, 
=0.11802
(The units are not important.)
Uniaxial tension, C3D8 elements.
Uniaxial tension with initial stress, C3D8 elements.
Uniaxial tension, CPS4 elements.
Uniaxial tension with initial stress, CPS4 elements.
Uniaxial tension, T3D2 elements.
Uniaxial tension with initial stress, T3D2 elements.
Elasticity
Young's modulus, E=300.0E3
Poisson's ratio, =0.3
Plasticity
The hyperbolic and exponent forms of the yield criteria are verified by using parameters that reduce them into equivalent linear forms. Reducing the hyperbolic yield function into a linear form requires that 
. Reducing the exponent yield function into a linear form requires that b=1.0 and that a=(
)–1.
Most tests in this section are set up as cases of the homogeneous deformation of a single element of unit dimensions. Consequently, the results are identical for all integration points within the element. To test certain conditions, however, it is necessary to set up inhomogeneous deformation problems. In each case the constitutive path is integrated with 20 increments of fixed size.
Uniaxial compression, C3D8 elements.
Uniaxial compression, CPS4 elements.
Triaxial compression, CAX4 elements.
Triaxial extension, CAX4 elements.
K=0.78, triaxial extension, CAX4 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
K=0.78, shear, C3D8 elements.
K=0.78; shear, CPS4 elements.
Uniaxial tension, C3D8 elements.
Uniaxial tension, CPS4 elements.
K=0.78, uniaxial tension, C3D8 elements.
K=0.78, uniaxial tension, CPS4 elements.
K=0.78, uniaxial tension with temperature dependence, C3D8R elements.
Hydrostatic tension, C3D8 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Triaxial stress, CPS4 elements (inhomogeneous).
K=0.78, triaxial stress, CPE4 elements (inhomogeneous).
K=0.78, triaxial stress, CPS4 elements (inhomogeneous).
Uniaxial compression with temperature dependence, C3D8 elements.
Linear perturbation uniaxial compression, C3D8 elements.
Uniaxial compression with rate dependence, C3D8 elements.
Uniaxial compression with nonzero initial condition for , C3D8 elements.
Uniaxial tension, perfect plasticity, CPS4 elements.
Hydrostatic tension, C3D8 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Triaxial extension, CAX4 elements.
Uniaxial tension, C3D8 elements.
Uniaxial tension, CPS4 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
Triaxial compression, CAX4 elements.
Uniaxial compression, C3D8 elements.
Uniaxial compression, CPS4 elements.
Uniaxial compression with rate dependence, C3D8 elements.
Uniaxial compression with temperature dependence, C3D8 elements.
Linear perturbation uniaxial compression, C3D8 elements.
Hydrostatic tension, C3D8 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Triaxial extension, CAX4 elements.
Uniaxial tension, C3D8 elements.
Uniaxial tension, CPS4 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
Triaxial compression, CAX4 elements.
Uniaxial compression, C3D8 elements.
Uniaxial compression, CPS4 elements.
Uniaxial compression with rate dependence, C3D8 elements.
Linear perturbation uniaxial compression, C3D8 elements.
Hydrostatic tension, C3D8 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Triaxial extension, CAX4 elements.
Uniaxial tension, C3D8 elements.
Uniaxial tension, CPS4 elements.
Shear, C3D8 elements.
Shear, CPS4 elements.
Triaxial compression, CAX4 elements.
Uniaxial compression, C3D8 elements.
Uniaxial compression, CPS4 elements.
Uniaxial compression with rate dependence, C3D8 elements.
Uniaxial compression with temperature dependence, C3D8 elements.
Linear perturbation uniaxial compression, C3D8 elements.
Elasticity
Logarithmic bulk modulus, 
=1.49
Poisson's ratio, =0.1
Plasticity
Initial conditions
Initial void ratio, 
=4.1
The hyperbolic and exponent forms of the yield criteria are verified by using parameters that reduce them into equivalent linear forms. Reducing the hyperbolic yield function into a linear form requires that . Reducing the exponent yield function into a linear form requires that b=1.0 and that a=()–1.
(The units are not important.)
The tests in this section are set up as cases of homogeneous deformation of a single element of unit dimensions. Consequently, the results are identical for all integration points within the element. In each case the constitutive path is integrated with 20 increments of fixed size.
Uniaxial strain, CAX4 elements.
Triaxial compression, CAX4 elements.
Uniaxial strain, CAX4 elements.
Triaxial compression, CAX4 elements.
Uniaxial strain, CAX4 elements.
Triaxial compression, CAX4 elements.
Uniaxial strain, CAX4 elements.
Triaxial compression, CAX4 elements.
In the tests described in this section, the following data for linear elasticity, cap plasticity I, cap hardening I, and K=1.0 are used unless otherwise specified. With this data, the elastic shear modulus is 5000.0 and the bulk modulus is 10000.0. First yield in pure shear occurs at S12=100.0, first yield in pure hydrostatic compression occurs at PRESS=270.0, first yield in pure hydrostatic tension occurs at PRESS=300.0, and first yield with PRESS=
occurs at PRESS=120.0 and S12=125.0. C3D8 elements are used unless otherwise specified.
Linear elasticity (used in nearly all tests)
Young's modulus, E=12857.1429
Poisson's ratio, =0.28571429 (= 1/7)
Cap plasticity I (used in nearly all tests)
Cohesion, d=173.20508 (= 100
)
Slope of Drucker-Prager failure surface, 
=30.0
Cap ellipticity, R=0.61858957
Initial volumetric plastic strain, 
=0.027
Transition parameter, =0.69258232
Third invariant factor, K=1.0 or 0.8, depending on the test.
Cap hardening I (used in nearly all tests)
Cap plasticity II
d=0.2286E6
=85.0
R=0.0875
=1.22
=0.07877
K=1.0
Cap hardening II
Porous elasticity I
Logarithmic bulk modulus, =20.0
Poisson's ratio, =0.28571429
Tensile strength limit, 
=1.0E5
Porous elasticity II
=0.09
=0.0
=0.02E6
Initial conditions
Initial void ratio, =1.0
Hydrostatic cyclic test, displacement control.
The following six steps are executed:
Load, yielding in hydrostatic compression
Unload, still in compression
Reload, yielding in compression
Unload in compression and load, yielding in tension
Unload in tension and load, yielding in compression
Unload
Uniaxial compressive stress test; displacement control.
Step 2 reverses the displacement causing yielding in tension.
Shear test; load control (S22=–S11); overlaid soft linear element.
There will be some hydrostatic stress due to transverse restraint.
Cyclical shear test; displacement control; S12 dominant.
Hydrostatic compression to 
, then pure shear; displacement control; temperature dependence.
Yielding should be volume preserving.
Shear test; load control; two primary elements and two overlaid soft elements.
One set loaded with principal stresses 
(1, 1, –2), the other with (–1, –1, 2).
The ratio of yield stresses should be K=0.8.
Uniaxial compressive strain (odometer) test; CPE4 element; load control; with temperature and field variable dependence of the *CAP PLASTICITY and *CAP HARDENING data.
The temperatures and field variables are specified to give *CAP PLASTICITY and *CAP HARDENING data exactly the same as cap plasticity I and cap hardening I data.
Uniaxial compressive strain (odometer) test; load control; NLGEOM and porous elasticity I.
The tangent bulk and shear moduli of porous elasticity I differ from that of the linear elasticity by about 1% over the strain range of the test.
Triaxial test. Hydrostatic loading to , then increase S11 only.
Uniaxial compressive strain (odometer) test; load control; the nonlinear analysis is split into two steps, each of which is preceded by a linear perturbation step.
The results of the nonlinear steps should correspond to those of mca0003bus.inp.
The results of the two linear perturbation steps (*STATIC) should be identical because small displacements are assumed and the elasticity is linear.
A displacement pattern designed to produce different stress states at the 8 Gauss points but dominated by shear.
The aim is to test the robustness of the Newton loops, so very large strain increments are taken.
Displacement control. K=0.8.
Another test of the robustness of the algorithm.
CAX4 element, porous elasticity II, cap plasticity II, and cap hardening II is used.
Tests adjustment of the initial position of the cap.
Two C3D8R elements with different initial stress states.
The initial stress in element 1 will cause an adjustment that will make the stress point lie on the cap yield surface.
The initial stress in element 2 will cause an adjustment that will make the stress point lie on the transition yield surface.
Porous elasticity
Logarithmic bulk modulus, =0.026
Poisson's ratio, =0.3
Plasticity
Logarithmic plastic bulk modulus, 
=0.174
Critical state slope, M=1.0
Initial yield surface size, 
=58.3
(except in tests mclxxxxahc.inp where we use =130.9 or 
=1.904)
Cap parameter, =0.5 (when included; otherwise, 1.0)
Third invariant ratio, K=0.78 (when included; otherwise, 1.0)
Initial conditions
Initial void ratio, =1.08
(The units are not important.)
Hydrostatic compression, C3D8 elements.
Hydrostatic compression with intercept option, C3D8 elements.
Triaxial compression, CAX8R elements.
Triaxial compression, temperature dependence, CAX8R elements.
=0.5, triaxial compression, CAX8R elements.
Triaxial extension, CAX8R elements.
K=0.78, triaxial extension, CAX8R elements.
K=0.78, triaxial extension, field variable dependence, CAX8R elements.
=0.5, K=0.78, triaxial extension, CAX8R elements.
Uniaxial compression, CAX8R elements.
Shear, C3D8 elements.
Shear, tabulated hardening, C3D8 elements.
Linear perturbation hydrostatic compression, C3D8 elements.
Elasticity
Young's modulus, E=3.0E6
Poisson's ratio, =0.2
Plasticity
Initial yield stress in hydrostatic compression, 
=2.0E5
Strength in hydrostatic tension, =2.0E4
Initial yield stress in uniaxial compression, 
=2.2E5
Yield stress ratio, 
=1.1
Yield stress ratio, 
=0.1
Hardening curve (from uniaxial compression):
Initial conditions
Initial volumetric compacting plastic strain, 
, is set to 0.02 for the cases in which the TYPE=HARDENING parameter on the *INITIAL CONDITIONS option is tested.
(The units are not important.)
Hydrostatic compression, C3D8 elements.
Uniaxial compression, C3D8 elements.
Shear, C3D8 elements.
Uniaxial tension, C3D8 elements.
Uniaxial compression, CPE4 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Linear perturbation with *LOAD CASE and hydrostatic compression, C3D8 elements.
Elasticity
The Young's modulus used in each test is given in the input file description. The modulus of each test is based on the average elastic stiffness of the equivalent test with porous elasticity at increments 10 and 20. A direct comparison with the results documented in “Drucker-Prager plasticity with linear elasticity” in “Rate-independent plasticity in ABAQUS/Standard,” Section 2.2.9 is, therefore, possible.
Poisson's ratio, =0.3
Plasticity
Critical state slope, M=1.0
Initial volumetric plastic strain, 
=0.4
Cap parameter, =0.5 (when included; otherwise, 1.0)
Third invariant ratio, K=0.78 (when included; otherwise, 1.0)
The exponential hardening curve used in “Drucker-Prager plasticity with linear elasticity” in “Rate-independent plasticity in ABAQUS/Standard,” Section 2.2.9 is entered in tabulated form with an initial volumetric plastic strain that corresponds to a yield surface size of either =58.3 or =130.9.
(The units are not important.)
Hydrostatic compression, C3D8 elements, E=18820.
Triaxial compression, CAX8R elements, E=30732.
=0.5, triaxial compression, CAX8R elements, E=29556.
Triaxial extension, CAX8R elements, E=21114.
K=0.78, triaxial extension, CAX8R elements, E=28140.
=0.5, K=0.78, triaxial extension, CAX8R elements, E=27580.
Uniaxial compression, CAX8R elements, E=30000.
Shear, C3D8 elements, E=2798.
Linear perturbation with *LOAD CASE and hydrostatic compression, C3D8 elements, E=18820.
Elasticity
Young's modulus, E=300.0
Poisson's ratio, =0.3
Plasticity
Porous metal plasticity
Modified Gurson's model: 
=1.5, 
=1.0, 
=2.25
(otherwise, ===1.0)
Void nucleation parameters (when included): 
=0.3, 
=0.1, 
=0.04
Initial relative density, 
=0.95 (
=0.05).
Material properties used in coupled temperature-displacement analysis:
Elasticity
Young's modulus, E=200.0E9
Poisson's ratio, =0.3
Porous metal plasticity
===1.0
Initial relative density, =0.95 (=0.05).
Thermal properties
Specific heat, 
=586.0
Density, 
=7833.0
Conductivity, k=52.0
Coefficient of expansion, =1.2E–5
(The units are not important.)
Inhomogeneous deformation, displacement control, CPE4 elements.
Same as mgrono2xmx.inp except that the initial relative density is specified using the *INITIAL CONDITIONS, TYPE=RELATIVE DENSITY option.
Uniaxial tension, traction control, nucleation of voids, C3D8 elements.
Hydrostatic tension, displacement control, nucleation of voids, C3D8 elements.
Uniaxial strain (confined compression), traction control, CAX4 elements.
Uniaxial compression, traction control, CAX4 elements.
Shear, CPE4 elements.
Uniaxial tension, displacement control, CAX4 elements.
Hydrostatic tension, displacement control, CAX4 elements.
Shear, C3D8 elements.
Hydrostatic tension, displacement control, C3D8 elements.
Modified Gurson's model, uniaxial tension, displacement control, nucleation of voids, CAX4 elements.
Modified Gurson's model, hydrostatic compression, displacement control, CAX4 elements.
Uniaxial tension, coupled temperature-displacement, CAX4T elements.
Uniaxial tension, displacement control, CAX4 elements, temperature and field variable dependencies.
Modified Gurson's model, uniaxial tension, nucleation of voids, temperature dependencies.
Elasticity
Young's modulus, E=300.E3
Poisson's ratio, =0.3
Plasticity
(The units are not important.)
Hydrostatic tension, C3D8 elements.
Triaxial stress, CPE4 elements (inhomogeneous).
Triaxial extension, CAX4 elements.
Uniaxial tension, C3D8 elements.
Shear, C3D8 elements.
Triaxial compression, CAX4 elements.
Uniaxial compression, C3D8 elements.
Uniaxial compression with temperature dependence, C3D8 elements.
Linear perturbation steps containing *LOAD CASE, uniaxial compression, C3D8 elements.
Elasticity
Young's modulus, E=14.773E6
Poisson's ratio, =0.2273
Plasticity
Plastic “Poisson's ratio,” 
=0.039
Hardening curves: The hardening curves in tension and compression are illustrated in Figure 2.2.9–1.
Thermal properties
Specific heat, =47.52
Density, =439.92
Conductivity, k=9.4
Coefficient of expansion, =11.0E–6
(The units are not important.)
Most tests in this section are set up as cases of the homogeneous deformation of a single element of unit dimensions. Consequently, the results are identical for all integration points within the element.
Hydrostatic tension, C3D8 elements.
Shear, C3D8 elements.
Uniaxial tension, CAX4 elements.
Uniaxial compression with temperature dependence, C3D8 elements.
Uniaxial tension, coupled temperature-displacement, CAX4T elements.
Inhomogeneous deformation, CPE4 elements.
Uniaxial tension and linear perturbation steps containing *LOAD CASE , T3D2 elements.
=40.0
=40°