In this contribution, the phase change of unvulcanized to vulcanized rubber is described by a thermo-mechanical material model within the finite element method (FEM) framework. Before the vulcanization process (curing), rubber exhibits an elasto-visco-plastic behaviour with significant irreversible deformations without a distinct yield surface. After exposing rubber to high temperature, the molecular chains build-up crosslinks among each other and its mechanical behaviour changes to stiffer viscoelastic material. The proposed model assumes, that both phases are present during the vulcanization process. The ratio changes from the uncured phase at the beginning to the cured phase according to the current state of cure. A constitutive curing formulation is introduced into the model, to capture the shape change during the vulcanization and to ensure, that the second law of thermodynamics is fulfilled. A multiplicative split of the deformation gradient is assumed to describe incompressible material. Thermal expansion due to the change of temperature is taken into account in the volumetric part, as well as shrinkage during the vulcanization process. In the isochoric part, the phase change from elasto-visco-plastic to viscoelastic material is described by micro-macro transition based on the micro-sphere model. The consistent formulation of the material model and its tangent are important for a successful implementation into a three-dimensional finite strain FEM framework. The capabilities of the model are shown by the simulation of an axisymmetric tire production process starting at the green tire inserted into the heating press up to a post-cure inflation step.

中文翻译：

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用于橡胶硫化和轮胎制造仿真的热机械材料模型

在此贡献中，未硫化橡胶到硫化橡胶的相变由有限元方法 (FEM) 框架内的热机械材料模型描述。在硫化过程（固化）之前，橡胶表现出弹粘塑性行为，具有显着的不可逆变形，没有明显的屈服面。将橡胶暴露在高温下后，分子链相互之间建立交联，其机械行为改变为更硬的粘弹性材料。所提出的模型假设在硫化过程中存在两个相。根据当前的固化状态，该比率从开始时的未固化阶段变为固化阶段。在模型中引入了本构硫化配方，以捕捉硫化过程中的形状变化并确保，即满足热力学第二定律。假定变形梯度的乘法分裂来描述不可压缩材料。体积部分考虑了由于温度变化引起的热膨胀，以及硫化过程中的收缩。在等容部分，从弹-粘-塑性材料到粘弹性材料的相变是基于微球模型通过微宏观转变来描述的。材料模型及其切线的一致公式对于成功实施到三维有限应变 FEM 框架中很重要。该模型的功能通过对轴对称轮胎生产过程的模拟来展示，该过程从插入热压机的生胎开始，直至硫化后充气步骤。