Numerical Modelling and Biaxial Tests for the Mullins Effect in Rubber

The formulation, testing and numerical study of the Mullins effect on rubber are presented. Ogden first modelled the Mullins effect for studying the unloading in filled rubber. It has been extended here to include the Mullins effect on both unloading and subsequent loading. To demonstrate the Mullins effect experimentally, a new biaxial test, inflation of a plane circular membrane, is used. Some experimental test data are presented. An approximate solution, a relation between the inflation pressure and the displacement at the centre for the inflation of a plane circular membrane is presented. The test data and the approximate solution are used to determine the Mullins damage material constants. For more accurate study, the material constants can also be obtained through the combination of LS-DYNA, LS-OPT and the test data. The test data, analytical results and numerical results from LS-DYNA are shown. They agree with one another.