Finite Element and Mesh-Free Simulation Environment for the Molding and Vulcanization of Rubber in Industrial Tire Production

在过去的几年里(2018-2021年)，从研究项目意义上对轴对称汽车轮胎的成型和硫化过程的数值表示进行了密集的基础研究。在这个项目中，结构分析研究所(ISD)的申请者Michael Kaliske教授开发了一个基于有限元方法的热机械轮胎成型模拟环境，重点模拟了从未硫化到最终硫化的轴对称轮胎的成型过程。基于有限元(FE)的模拟方法使用任意拉格朗日欧拉(ALE)描述来跟踪生胎成型过程中的材料点，以获得成型过程的表示(避免网格变形)。此外，还发展了几种先进的热力耦合材料模型来描述橡胶的硫化和未硫化状态。然而，由于成型过程中未硫化橡胶的复杂几何形状、摩擦和材料流动(与现实3D轮胎设计的数值稳定性和稳健性有关的问题)，任意胎面花纹的成型仍然具有挑战性。这些开放的研究问题将是ISD和工业项目合作伙伴德国大陆莱茵集团之间转移项目的进一步发展步骤。该转移项目旨在结合基础学术研究和新产品创新实现程序的优势，在整个工艺链数字化的不断变化的工业环境中。因此，转让项目不仅将在项目意义上开发的模拟环境(未硫化和硫化橡胶的材料模型，橡胶成型的ALE方法，工业专业知识的交流)带入工业应用，而且将进一步促进高级数值方法的发展，通过另一种数值方法--材料点法(MPM)，对任意花纹轮胎从制造状态到使用状态的高级数值描述和表示。Transfer项目的其他新研究方面涉及作为一种无网格方法的隐式MPM的开发和应用，该方法用于在3D中对具有任意胎面图案的轮胎进行建模(用于胎面的MPM模拟)，在热力学框架中的MPM的公式，用于在成形和硫化过程(制造阶段)期间进行分析的有限元方法(轮胎主体)和MPM(轮胎胎面)的耦合，以及提出针对有限元、MPM或ALE的材料行为的实现的策略，包括描述当前材料状态(非弹性、非线性)。主要目标是开发一个强大的和数值稳定的模拟环境，用于三维轮胎花纹轮胎的成型和硫化。

In the last years (2018-2021), intensive fundamental research on the numerical representation of the molding and the vulcanization process of axisymmetric, automotive tires has been carried out in the research project SENSE. Within this project, a thermo-mechanical tire molding simulation environment by the finite element method (FEM) focusing on the simulation of the process from the uncured to the final cured axisymmetric tire has been developed by the applicant Prof. Michael Kaliske at the Institute for Structural Analysis (ISD). The finite element (FE) based simulation approach uses an Arbitrary Lagrangian Eulerian (ALE) description to track the material points during the molding of the green tire to obtain a representation of the molding process (avoidance of mesh distortion). Furthermore, several advanced thermo-mechanically coupled material models have been developed to describe rubber in its cured and uncured state. However, the molding of arbitrary tread patterns is still challenging due to the complex geometry, friction and the material flow of the uncured rubber during the molding process (questions with respect to numerical stability and robustness for realistic 3D tire designs). These open research questions shall be further development steps of this transfer project between ISD and the industrial project partner Continental Reifen Deutschland GmbH. The transfer project aims to combine the strengths of fundamental academic research and innovative realization procedures of new products in a changing industrial environment subjected to digitalization of the whole process chain. Hence, the transfer project will not only bring to industrial application the simulation environment developed within the project SENSE (material model for unvulcanized and vulcanized rubber, ALE approach for rubber molding, exchange on industrial expertise) but will further contribute to the development of numerical methods for the advanced numerical description and representation of tires with arbitrary tread patterns from their manufacturing state to their service state by an alternative numerical method, the material point method (MPM). Additional new research aspects of the transfer project address the development and application of the implicit MPM as a mesh-free method for the molding of tires with arbitrary tread pattern (MPM simulation for tread) in 3D, the formulation of the MPM in the framework of thermo-mechanics, a coupling of FE methods (tire main body) with the MPM (tire tread) for the analysis during the forming and vulcanization process (manufacturing stage), and a strategy to propose an implementation of the material behavior for FEM, MPM or ALE including the description of the current material state (inelastic, nonlinear). The main objective is the development of a robust and numerically stable simulation environment for the molding and vulcanization of tires with 3D tread patterns.