A Microsphere-Based Rubber Curing Model for Tire Production Simulation

Research output: Contribution to journalResearch articleContributedpeer-review



In this contribution, a constitutive model for rubber is presented that describes the material in its unvulcanized and vulcanized state as well as during its phase transition. The model is based on the microsphere approach to represent the three-dimensional macroscopic behavior by a set of one-dimensional microscopic chains. When the uncured rubber is exposed to large temperature, the polymer chains build-up crosslinks among each other and the material changes its properties from soft viscoplastic to stiffer viscoelastic behavior. The state of cure over time at different temperatures is identified via a moving die rheometer (MDR) test. Based on this experimental data, a kinetic model is fitted to represent the state of cure in the simulation. The material model changes from the description of an unvulcanized state to a vulcanized state based on the current degree of cure in a thermomechanically consistent manner and fulfills the second law of thermodynamics. The curing model framework is suitable to combine any given material models for uncured and cured rubber. The presented material formulation is applied to an axisymmetric tire production simulation. Therefore, the kinetic state of cure approach is fitted to MDR experimental data. The uncured and cured material model parameters are fitted separately to experiments by a gradient based fitting procedure. The in-molding and curing process of a tire production is simulated by a finite element approach. Subsequently, the simulated footprint of the tire is compared to experimental results. It can be shown that the quality of the footprint could be optimized solely by changing the shape of the green tire.


Original languageEnglish
Pages (from-to)82–113
Number of pages32
JournalTire Science and Technology
Issue number2
Publication statusPublished - 27 Jan 2023

External IDs

Mendeley 72f11115-8b28-3f6e-bd14-8aa4ca35e7e5