Constitutive Model of Filled Elastomers Capable of Capturing Mullins Effect, Hysteresis, Induced Anisotropy and Permanent Set – Part I: Model Theory & Implementation

In this contribution, a finite element implementation of a micromechanically based constitutive model describing several inelastic effects of filled rubbers in multiaxial deformation states is presented. The model describes the elastic and inelastic effects of filled rubbers and is based on the network decomposition concept. Accordingly, the rubber network is decomposed into an isotropic elastic network E, responsible for the polymer matrix, and two anisotropic permanent damage networks (M and H) which are responsible for the filler-polymer interaction. The anisotropic damage networks M and H are capable of capturing the Mullins effect, hysteresis, permanent set and induced anisotropic stress softening. This model is implemented into LS-DYNA® by means of a subroutine within *MAT_USER_DEFINED _MATERIAL_MODELS (UMAT). The user can easily switch between different combinations of elastic and inelastic models by activating and deactivating each network. The user can also select the number of directions to be considered depending on the complexity of the loading history. The model with appropriate material constants demonstrates good agreement with experimental data.