Product: ABAQUS/Standard
Material 1:
Polynomial coefficients (N=1):  = 8.,  = 2. |
Compressible case:  = 0.1. |
Prony series coefficients (N=1):  = 0.,  = 0.5,  = 3. |
Material 2:
| Polynomial coefficients (N=1): = 8., = 2. |
| Compressible case: = 0.1. |
| Prony series coefficients (N=1): = 0.5, = 0., = 3. |
| Heat transfer properties for coupled analysis: conductivity = 0.01, density = 1., |
| specific heat = 1. |
Material 3:
| Polynomial coefficients (N=1): = 1.5 × 106, = 0.5 × 106. |
| Compressible case: = 1. × 10–7. |
| Prony series coefficients (N=2): |
| = 0.5, = 0., = 0.2. |
 = 0.49,  = 0.,  = 0.5. |
Material 4:
| Polynomial coefficients (N=1): = 27.02, = 1.42. |
| Compressible case: = 0.000001. |
| Prony series coefficients (N=2): |
| = 0.25, = 0.25, = 5. |
| = 0.25, = 0.25, = 10. |
| Creep compliance test data generated from Prony series above. |
| Stress relaxation test data generated from Prony series above. |
Material 5:
| Polynomial coefficients (N=1): = 8., = 2. |
| Compressible case: = 0.001. |
| Prony series coefficients (N=2): |
| = 0.5, = 0., = 1. |
| = 0.49, = 0., = 2. |
Material 6:
| Polynomial coefficients (N=1): = 550.53, = –275.265. |
| Compressible case: = 7. × 10–7. |
| Prony series coefficients (N=6): |
| = 0.1986, = 0., = 0.281 × 10–7. |
| = 0.1828, = 0., = 0.281 × 10–5. |
 = 0.1388,  = 0.,  = 0.281 × 10–3. |
 = 0.2499,  = 0.,  = 0.281 × 10–1. |
 = 0.1703,  = 0.,  = 0.281 × 101. |
 = 0.0593,  = 0.,  = 0.281 × 103. |
Material 7:
Ogden coefficients (N=2):  = 16.,  = 2.,  = 4.,  = –2. |
| Prony series coefficients (N=1): = 0.5, = 0., = 3. |
Material 8:
Material 9:
The results agree well with exact analytical or approximate solutions.
Calibration of Prony series parameters from frequency-dependent moduli and vice versa has been tested for Materials 1, 4, and 6 in various relaxation and steady-state dynamic analyses. The data conversion is performed automatically in ABAQUS. In the tests described below some of the time domain analyses are repeated using frequency-dependent moduli data and some of the frequency domain (steady-state dynamic) analyses are repeated using time-dependent moduli data. The results of the repeated analyses are in good agreement with those of the original.
Compressible, volumetric compression, CPS4 elements.
Compressible, volumetric compression, CPS4 elements; Prony series parameters calibrated from frequency-dependent moduli.
Compressible, volumetric compression, CPS4 elements; steady-state dynamic, frequency-dependent moduli data derived from specified Prony series parameters.
Compressible, volumetric compression, CPS4 elements; steady-state dynamic, direct specification of frequency-dependent moduli data.
Tabulated frequency-dependent moduli data used in mvhcdo2sr2.inp and mvhcdo2ss2.inp as an *INCLUDE file.
Compressible, volumetric compression, CPE4 elements.
Incompressible, uniaxial tension, coupled analysis, CPE4HT elements.
Incompressible, relaxation in uniaxial tension, CPS4 elements.
Incompressible, uniaxial tension, CPE4H elements.
Incompressible, triaxial, CPE4H elements.
Compressible, relaxation in uniaxial tension, CPE4 elements.
Compressible, uniaxial tension, static and relaxation, CPE4H elements.
Creep and relaxation test data, uniaxial tension, static and relaxation, 2 CPE4RH elements.
Compressible, uniaxial tension, static and relaxation, 2 CPE4RH elements; Prony series parameters calibrated from frequency-dependent moduli.
Creep and relaxation test data, compressible, uniaxial tension, steady-state dynamic, 2 CPE4RH elements.
Compressible, uniaxial tension, steady-state dynamic, 2 CPE4RH elements; direct specification of Prony series parameters calibrated in mvhtdo3ssd.inp.
Compressible, uniaxial tension, steady-state dynamic, 2 CPE4RH elements; frequency-dependent moduli data derived from Prony series parameters calibrated from shear relaxation and creep test data as used in mvhtdo3ssd.inp.
Tabulated frequency-dependent moduli data used in mvhtdo3ss3.inp as an *INCLUDE file.
Combined test data, uniaxial tension, static and relaxation, 2 CPE4RH elements.
Compressible, uniaxial tension and rotation, static and relaxation, CPS4 elements.
Compressible, uniaxial tension and rotation, static and relaxation with static linear perturbation steps containing *LOAD CASE, CPS4R elements.
Compressible, relaxation in uniaxial tension, M3D4 elements.
Compressible, biaxial compression tension, CAX4R elements.
Compressible, biaxial compression tension, CAX4R elements; Prony series parameters calibrated from frequency-dependent moduli.
Compressible, biaxial compression tension, CAX4R elements; steady-state dynamic, frequency-dependent moduli data derived from specified Prony series parameters.
Compressible, biaxial compression tension, CAX4R elements; steady-state dynamic, direct specification of frequency-dependent moduli data.
Tabulated frequency-dependent moduli data used in mvhcdo3kc2.inp and mvhcdo3ss2.inp as an *INCLUDE file.
Incompressible, relaxation in uniaxial tension, Ogden model, CPE4H elements.
Incompressible, uniaxial tension with static linear perturbation steps, Ogden model, CPE4H elements.
Incompressible, relaxation in uniaxial tension, Arruda-Boyce model, CPE4H elements.
Incompressible, uniaxial tension with static linear perturbation steps containing *LOAD CASE, Arruda-Boyce model, CPE4H elements.
Incompressible, relaxation in uniaxial tension, Van der Waals model, CPE4H elements.
Incompressible, uniaxial tension with static linear perturbation steps, Van der Waals model, CPE4H elements.
Material 1:
| Hyperfoam coefficients (N=3): |
= –17.4, = –1.22, = 548.2, = 17.3,  = 10.47,  = –1.775,  =  =  = 0. |
| Prony series coefficients (N=1): = 0.5, = 0., = 3. |
Material 2:
Compressible, relaxation in uniaxial tension, CPE4 elements.
Compressible, uniaxial tension with static linear perturbation steps containing *LOAD CASE, CPE4 elements.
Compressible, relaxation in uniaxial tension, CPE4 elements.
Material 1:
| Young's modulus = 200 GPa. |
| Poisson's ratio = 0.3. |
| Density = 8000 kg/m3. |
| Fourier transform coefficients (tabular): |
 = 1.161 × 10–2,  = –3.21 × 10–2,  = 0,  = 0,  = 1. |
 = 7.849 × 10–3,  = –2.222 × 10–2,  = 0,  = 0,  = 15.8. |
 = 5.354 × 10–3,  = –1.533 × 10–2,  = 0,  = 0,  = 25.1. |
 = 3.639 × 10–3,  = –1.062 × 10–2,  = 0,  = 0,  = 39.8. |
 = 2.543 × 10–3,  = –7.382 × 10–3,  = 0,  = 0,  = 63.1. |
 = 1.775 × 10–3,  = –5.116 × 10–3,  = 0,  = 0,  = 100. |
Material 2:
| Young's modulus = 200 GPa. |
| Poisson's ratio = 0.3. |
| Density = 8000 kg/m3. |
| Fourier transform coefficients (formula): |
 = 2.3508 × 10–3,  = 6.5001 × 10–3,  = 1.38366,  =  =  = 0. |
Material 3:
| Polynomial coefficients (N=1): = 33.333333 × 109, = 0, = 12.0 × 10–12. |
| Fourier transform coefficients (tabular): |
| = 1.161 × 10–2, = –3.21 × 10–2, = 0, = 0, = 1. |
| = 7.849 × 10–3, = –2.222 × 10–2, = 0, = 0, = 15.8. |
| = 5.354 × 10–3, = –1.533 × 10–2, = 0, = 0, = 25.1. |
| = 3.639 × 10–3, = –1.062 × 10–2, = 0, = 0, = 39.8. |
| = 2.543 × 10–3, = –7.382 × 10–3, = 0, = 0, = 63.1. |
| = 1.775 × 10–3, = –5.116 × 10–3, = 0, = 0, = 100. |
Material 4:
| Polynomial coefficients (N=1): = 33.333333 × 109, = 0, = 12.0 × 10–12. |
| Fourier transform coefficients (formula): |
| = 2.3508 × 10–3, = 6.5001 × 10–3, = 1.38366, = = = 0. |
Material 5:
| Polynomial coefficients (N=1): = 33.333333 × 109, = 0, = 12.0 × 10–12. |
| Fourier transform coefficients (formula): |
| = 2.3508 × 10–3, = 6.5001 × 10–3, = 0, = = = 0. |
Material 6:
Arruda-Boyce coefficients:  = 66.6666 × 109,  = 5. ,  = 12.0 × 10–12. |
| Fourier transform coefficients (tabular): |
| = 1.161 × 10–2, = –3.21 × 10–2, = 0, = 0, = 1. |
| = 7.849 × 10–3, = –2.222 × 10–2, = 0, = 0, = 15.8. |
| = 5.354 × 10–3, = –1.533 × 10–2, = 0, = 0, = 25.1. |
| = 3.639 × 10–3, = –1.062 × 10–2, = 0, = 0, = 39.8. |
| = 2.543 × 10–3, = –7.382 × 10–3, = 0, = 0, = 63.1. |
| = 1.775 × 10–3, = –5.116 × 10–3, = 0, = 0, = 100. |
Material 7:
| Arruda-Boyce coefficients: = 66.6666 × 109, = 5. , = 12.0 × 10–12. |
| Fourier transform coefficients (formula): |
| = 2.3508 × 10–3, = 6.5001 × 10–3, = 1.38366, = = = 0. |
Material 8:
Van der Waals coefficients: = 66.6666 × 109, = 10. , = 0.1,  = 0., = 12.0 × 10–12. |
| Fourier transform coefficients (tabular): |
| = 1.161 × 10–2, = –3.21 × 10–2, = 0, = 0, = 1. |
| = 7.849 × 10–3, = –2.222 × 10–2, = 0, = 0, = 15.8. |
| = 5.354 × 10–3, = –1.533 × 10–2, = 0, = 0, = 25.1. |
| = 3.639 × 10–3, = –1.062 × 10–2, = 0, = 0, = 39.8. |
| = 2.543 × 10–3, = –7.382 × 10–3, = 0, = 0, = 63.1. |
| = 1.775 × 10–3, = –5.116 × 10–3, = 0, = 0, = 100. |
Material 9:
The problem involves a direct-integration steady-state dynamic procedure in which a harmonic pressure of amplitude 1.0 GPa is applied to the top surface of a cantilevered beam. Several subspace-based steady-state dynamic procedures follow to test several parameters on the *STEADY STATE DYNAMICS option. The results of most interest are the vertical displacement at the tip of the cantilever and the phase angles of the displacements for the specified frequencies.
Tabular frequency domain viscoelasticity, elastic, CPS4 elements.
Tabular frequency domain viscoelasticity, elastic, C3D8 elements.
Formula frequency domain viscoelasticity, elastic, CPS4 elements.
Formula frequency domain viscoelasticity, elastic, C3D8 elements.
Tabular frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Tabular frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Formula frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Formula frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Formula frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Formula frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Tabular frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Tabular frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Formula frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Formula frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Tabular frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Tabular frequency domain viscoelasticity, hyperelastic, C3D8 elements.
Formula frequency domain viscoelasticity, hyperelastic, CPS4 elements.
Formula frequency domain viscoelasticity, hyperelastic, C3D8 elements.