Tire production is a complex process due to large deformations, highly non-linear uncured rubber material and large temperature. It can be observed, that the production conditions have a strong influence on the cured tire behaviour and should be studied to minimize possible defects in the final product. In this contribution, an Arbitrary Lagrangian Eulerian (ALE) formulation is presented to overcome convergence issues stemming from large distortion of elements in a pure Lagrangian description. In an ALE formulation, the computational mesh is not fixed in space and can move relatively to the material motion, which allows to control the distortion of the mesh by a smoothing algorithm. Coupling the material motion with the newly obtained mesh is done by an advection algorithm to project the internal variables of a thermo-mechanically consistent material model. Based on the assumption that the internal variables are projected directly from the integration points, an additional mesh is generated with the integration points of the old mesh as grid. To show the capabilities of the presented algorithm, several numerical examples are shown ranging from a simple forging example to a complex tire production process.

由于大变形、高度非线性的未硫化橡胶材料和高温，轮胎生产是一个复杂的过程。可以观察到，生产条件对硫化轮胎的性能有很大影响，应进行研究以尽量减少最终产品中可能存在的缺陷。在这篇文章中，提出了一种任意拉格朗日欧拉 (ALE) 公式，以克服由纯拉格朗日描述中的元素大失真引起的收敛问题。在 ALE 公式中，计算网格在空间中不是固定的，可以相对于材料运动移动，这允许通过平滑算法控制网格的变形。通过平流算法将材料运动与新获得的网格耦合，以投影热机械一致材料模型的内部变量。基于内部变量直接从积分点投影的假设，以旧网格的积分点为网格生成额外的网格。为了展示所提出算法的能力，展示了几个数值示例，从简单的锻造示例到复杂的轮胎生产过程。