Investigation of the viscoelastic material behaviour of filled elastomers under multiaxial deformations

如今，填充橡胶材料在工业装配中扮演着重要的角色。聚合物块体材料和填料颗粒的不同可能组合的多样性可以影响材料的行为，以达到应用的要求，这表明了这种材料类别的相关性。在我们的项目中，我们将研究一种炭黑填充的三元乙丙橡胶作为填充橡胶类的代表性材料。研究证明，应力-应变关系对于不同的弹性体-填料组合是可传递的。使用关于应变不变量的系列方法的宏观和唯象模型将描述该材料。早期对准静态行为的研究表明，关于单轴实验的描述通常不能显示一般的双轴加载状态，以及仅依赖于第一不变量的描述。如果使用单轴模型开发，即使只考虑弹性行为，多轴模拟也不匹配。如果仔细观察实际应用，即使宏观加载条件非常简单，例如仅单轴加载，组件复杂的几何形状也会导致复杂的变形状态。应变条件的这种局部变化也导致在加载过程中整个几何形状上的应变率分布的变化。事实上，必须指出的是，在这种多轴加载条件下的粘弹性行为在这方面起着重要的作用。填充橡胶材料通常表现出明显的粘弹性行为，强烈影响材料的整体行为。关于多轴变形的尽可能一般的材料描述也需要非常广泛的实验研究。因此，对于准静态加载条件和动态加载条件，我们都将使用双向拉伸试验。因此，必须考虑不同的加载路径，以表示关于加载历史的材料存储器的时间依赖性。必要的实验次数和特有的长松弛时间在一个复杂的实验过程中产生。为此，我们将开发一种新的实验过程，允许为材料模型提供尽可能多的信息，但也不会提供太多信息。我们的目标是做尽可能少的实验，但也要尽可能多地进行实验，这在进一步的模型和参数识别中也必须考虑在内。所得到的材料模型应该尽可能通用，以便正确地表示多轴变形。必须研究模型方法的形状，包括关于依赖时间的多轴性的这一一般性。数值实现将在一个开源的有限元代码中实现。

Nowadays filled rubber materials play an important role in industrial assemblies. The diversity in the different possible combinations of polymer bulk materials and filler particles can influence the material behavior to achieve the requirements of the application which shows the relevance of this material class. In our project we will investigate a carbon black-filled EPDM as a representative material for the class of filled rubber. Investigations have proved the transferability of the stress-strain relations to different elastomer-filler combinations. A macroscopical and phenomenological model using a series approach with respect to the strain invariants will describe the material. Earlier investigations of the quasistatic behavior have shown, that a description with respect to uniaxial experiments is usually not able to display general biaxial loading states as well as a description which is only dependent on the first invariant. Multiaxial simulations do not match if a uniaxial modell development is used, even taking into account elastic behavior only. If a detailed look on real applications is taken, the assemblies complex geometries result in complex deformation states even if the macroscopical loading condition is quite simple, for example only uniaxial. This local variation of the strain conditions also results in a variation of the strain rates distributed over the whole geometry during the loading. As a fact, it has to be pointed out that the viscoelastic behavior for such multiaxial loading conditions plays an important role in this context. Filled rubber materials usually show a pronounced viscoelastic behavior strongly influencing the overall material behavior. An as general as possible material description with respect to multiaxial deformations requires a very broad experimental investigation as well. Hence, we will use the biaxial tensile test regarding both, quasistatical loading conditions as well as dynamical loadings. Hereby different loading paths have to be taken into account to represent the time dependency with respect to the material memory concerning the loading history. The number of necessary experiments and the characteristical long relaxation times yield in a complex experimental procedure. For that purpose, we will develop a new experimental process which allows as much information as possible for the material model, but also not too much information. Our goal is to do as less experiments as possible, but also as much as necessary, which also have to be taken into account in the further model and parameter identification. The resulting material model is supposed to be as general as possible in order to represent multiaxial deformations properly. The shape of the model approach has to be investigated including this generality with respect to time-dependent multiaxiality. The numerical realization will be implemented in an open-source FE-code.