Bergström-Boyce hysteresis for elastomers: test of time-dependent behavior
Elements tested
CAX4
CPE4
Problem description
The problems in this set are simulations of experiments presented in Bergström and Boyce (1998). The Abaqus/Standard results are compared to the Bergström and Boyce results.
The tests consist of uniaxial compression of disk-like rubber specimens (height = 13 mm, diameter = 28 mm) and plane strain compression of rectangular specimens (height = 13 mm, cross-sectional area = 140 mm2). The materials used in the tests are Chloroprene rubber with varying carbon black filler concentrations and unfilled Nitrile rubber. The specimens are subjected to constant strain rate, cyclic loading, and constant strain-rate load cycles interspersed with relaxation segments of varying time intervals. The strain measure used here refers to logarithmic strain.
Two problems that test the creep strain-rate regularizing parameter, E, have also been included.
Material:
- Arruda-Boyce hyperelasticity
-
Chloroprene rubber (15 pph. carbon black) = 0.6 MPa, = = 2.8284, D = 0.01 Chloroprene rubber (40 pph. carbon black) = 1.08 MPa, = = 2.8284, D = 0.01 Chloroprene rubber (65 pph. carbon black) = 1.71 MPa, = = 2.8284, D = 0.01 Nitrile rubber (unfilled) = 0.87 MPa, = = 2.4495, D = 0.01 - Hysteresis
-
Chloroprene rubber (15 pph. carbon black) S = 1.6, A = 0.9526 (MPa)−4 s−1, m = 4.0, C = −1.0 Chloroprene rubber (40 pph. carbon black) S = 2.0, A = 0.9526 (MPa)−4 s−1, m = 4.0, C = −1.0 Chloroprene rubber (65 pph. carbon black) S = 4.0, A = 0.03135 (MPa)−5 s−1, m = 5.0, C = −0.9 Nitrile rubber (unfilled) S = 2.5, A = 0.5500 (MPa)−5 s−1, m = 5.0, C = −0.6
Loading:
The loading is imposed with displacement-controlled boundary conditions.
Results and discussion
The results of the Abaqus/Standard numerical simulations are in very good agreement with the results presented in Bergström and Boyce (1998). The results for the problems that test the creep strain-rate regularizing parameter, E, are almost identical to the results without the use of this parameter in all regions except around zero strain, where the results with this parameter are smoother.
Input files
- mbbcdo3euc_un_1e_2_cl15.inp
-
Uniaxial cyclic compression, linear perturbation with LOAD CASE, CAX4 elements; repeated cycling; strain rate = −0.01/s; Chloroprene rubber (15 pph. carbon black).
- mbbcdo3mcy_ps_1e_2_cl65.inp
-
Plane strain cyclic compression, CPE4 elements; strain rate = −0.01/s; Chloroprene rubber (65 pph. carbon black).
- mbbcdo3mcy_un_1e_2_cl15.inp
-
Uniaxial cyclic compression, CAX4 elements; strain rate = −0.01/s; Chloroprene rubber (15 pph. carbon black).
- mbbcdo3mcy_un_1e_2_cl40.inp
-
Uniaxial cyclic compression, CAX4 elements; strain rate = −0.01/s; Chloroprene rubber (40 pph. carbon black).
- mbbcdo3mcy_un_1e_2_cl65.inp
-
Uniaxial cyclic compression, CAX4 elements; strain rate = −0.01/s; Chloroprene rubber (65 pph. carbon black).
- mbbcdo3mcy_un_1e_2_ni.inp
-
Uniaxial cyclic compression, CAX4 elements; strain rate = −0.01/s; Nitrile rubber (unfilled).
- mbbcdo3mcy_un_23e_5_ni.inp
-
Uniaxial cyclic compression, CAX4 elements; strain rate = −0.00023/s; Nitrile rubber (unfilled).
- mbbcdo3rcy_un_1e_1_cl15.inp
-
Uniaxial cyclic compression with 1 relaxation segment in both uploading and unloading; relaxation strain = −0.6; strain rate = −0.1/s; relaxation time = 1000s; Chloroprene rubber (15 pph. carbon black).
- mbbcdo3ruc_un_1e_1_cl15.inp
-
Uniaxial cyclic compression with two relaxation segments in both uploading and unloading; relaxation strains = −0.26 and −0.54; strain rate = −0.1/s; relaxation time = 30s; Chloroprene rubber (15 pph. carbon black).
- mbbcdo3rcy_un_2e_3_cl15.inp
-
Uniaxial cyclic compression with two relaxation segments in both uploading and unloading; relaxation strains = −0.3 and −0.6; strain rate = −0.002/s; relaxation time = 120s; Chloroprene rubber (15 pph. carbon black).
- hysteresis_e001_uniaxial.inp
-
Cyclic uniaxial straining; test for creep strain-rate regularizing parameter E: CAX4 element.
- hysteresis_e001_biaxial.inp
-
Cyclic biaxial straining; test for creep strain-rate regularizing parameter E: C3D8R element.