Iran Polym J (2016) 25:89–109 DOI 10.1007/s13726-015-0405-5 1 3 REVIEW A state‑of‑the‑art review on the mathematical modeling and computer simulation of rubber vulcanization process Mir Hamid Reza Ghoreishy 1 Received: 14 March 2015 / Accepted: 14 June 2015 / Published online: 15 December 2015 © Iran Polymer and Petrochemical Institute 2015 Introduction Curing or vulcanization process is a fundamental step dur- ing the manufacturing of rubber articles, especially tires and other high thickness products. It plays an important role in achieving accurate and low tolerance shape and also pre-designed physical and mechanical properties of the final product. Therefore, optimum determination of time arrangements and temperature variations during heat- ing and cooling or post-cure steps is of prime importance. Moreover, due to high energy consumption of this stage, optimization also leads to more economical process. How- ever, owing to the low thermal diffusivity in rubbers and also applying time-varying operating conditions, the tem- perature field inside the article is not only non-uniform but also changes with time. Therefore, difficulties arise when a simple cure evaluation curve, generally obtained by a disk rheometer at constant temperature, is intended to be used to predict the time and temperature required for the com- pleteness of a curing process. Traditionally, a full experi- mental method is adopted in which the thermal history at various points inside the article (especially high thickness zones) is measured. The measured temperature can be converted to state of cure or degree of cure by the use of a kinetics equation, and thus, the time required to achieve a complete cycle is determined. Obviously, this method is time-consuming and expensive since for every experiment at least a rubber article should be damaged. Alternatively, determination of the thermal history and its variation inside a product by solving heat transfer equation using an appro- priate numerical method in conjunction with a computer code are the preferred methods in today’s rubber industry. Recently, we have briefly reviewed the numerical simula- tion of the curing process of rubber articles [1] and pre- sented some practical techniques to predict the temperature Abstract This monograph reviews and examines the theoretical background and literature published so far for the mathematical modeling and simulation of the rubber vulcanization process. This work has been organized in the following way. First, an introductory section is given, which provides a brief overview of the topic and the aim and scope of the paper. Then, it goes on to give a compre- hensive overview of the historical background up to present state. It is tried here not only to consider rubber vulcani- zation process, but the curing of other thermoset polymers are examined. The third section presents the mathematical modeling of the curing process and focuses on four key items including heat transfer governing equations, thermal properties of rubbers and their measurements, kinetics of the curing reaction and solution methodology. In this part, the details of the solution methods for the governing equa- tions and also different types of kinetics of curing reac- tions are studied. The fourth section presents the findings of some research works carried out in this field, which is divided into two subsections as tires and non-tires applica- tions. A brief summary on the presented work and some suggestions for future research are introduced in the fifth section, and finally the bibliography of this review is given. Keywords Rubber · Vulcanization · Simulation · Finite element method · Kinetics · Tire * Mir Hamid Reza Ghoreishy m.h.r.ghoreishy@ippi.ac.ir 1 Department of Rubber Processing and Engineering, Faculty of Processing, Iran Polymer and Petrochemical Institute, Tehran, P.O. Box 14975-112, Iran