Non-linear finite element damage modeling after multiple cyclic loading of rubberlike materials

This study presents a numerical implementation concept for elastomeric components under cyclic loading conditions at finite strains. Initial material damage is considered that is widely known as Mullins effect. A comprehensive quasi-static model is introduced and prepared for finite element implementation, covering both initial and subsequent loading cycles, converging to equilibrium. The combination of a non-linear relaxation-based hyperelastic model with selected damage functions allows for an accurate quantitative description of arbitrary elastomeric components. The study demonstrates the integration of the relaxed Modified Extended Tube Model (METM) in combination with Advanced Mullins Damage Modeling (AMDM) into a 3D finite element framework. Parameter studies and a relevant example from engineering practise prove the robustness of the finite element implementation and the applicability of the material modeling concept for virtually optimizing customized rubber compounds based on predefined elastomeric component properties.