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发挥着重要作用。聚合物本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行为以实现应用的要求，这显示了该材料类别的相关性。在我们的项目中，我们将研究炭黑填充EPDM作为填充橡胶类的代表材料。研究证明了应力-应变关系对不同填料-填料组合的可传递性。一个宏观的和唯象的模型，使用一系列的方法与应变不变量将描述的材料。早期的准静态行为的调查表明，相对于单轴实验的描述通常是不能显示一般的双轴加载状态以及描述，这是唯一依赖于第一个不变量。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。如果对真实的应用进行详细观察，则即使宏观加载条件相当简单，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还导致在加载期间分布在整个几何形状上的应变率的变化。事实上，必须指出的是，在这种多轴载荷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，强烈影响整体材料行为。关于多轴变形的尽可能通用的材料描述也需要非常广泛的实验研究。因此，我们将使用双轴拉伸试验，准静态加载条件以及动态加载。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记忆的时间依赖性。在复杂的实验过程中，需要进行大量的实验，而且弛豫时间很长。为此，我们将开发一种新的实验过程，该过程允许材料模型尽可能多的信息，但也不能太多。我们的目标是尽可能少的实验，但也尽可能多的必要，这也必须考虑到在进一步的模型和参数识别。由此产生的材料模型应该是尽可能通用的，以适当地表示多轴变形。模型方法的形状必须进行调查，包括这种一般性与时间相关的多轴性。数值实现将在开源FE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.