The mechanical response of filled rubber depends on load history, strain rate and state, temperature and even direction of previous loading. Although there is a plurality of both physical and phenomenological models, only few are able to reproduce this rich spectrum of effects. Moreover, many of them suffer from physical or mathematical inconsistencies. We present a model, which is based on physical ideas and plausible assumptions about the material’s microstructure, while being designed for high efficiency and robustness in finite element applications. It is shown by fits to extensive experimental data that it reproduces almost the full phenomenology of filled rubbers, both at low and high strains, for different deformation states and rates, holding times, and at different temperatures. The main modeling paradigm is the stress-induced breakdown and reorganization of microscopic structures which defines the time-dependent behavior of the material and allows to reproduce logarithmic relaxation effects. Moreover, its nine fit parameters evolve in a physically reasonable way under variation of filler and cross-linker content. A static limiting case of the model is derived, reducing the number of parameters and computational effort wherever necessary. Finally, a FE-implementation using computer-generated subroutines is presented and tested against experimental data of a simplified bushing under torsional, radial, cardanic and axial loading.

填充橡胶的机械响应取决于载荷历史，应变率和状态，温度以及先前载荷的均匀方向。尽管物理模型和现象模型都有很多，但只有少数几个能够重现这种丰富的效应。而且，其中许多遭受物理或数学上的不一致。我们提出了一个模型，该模型基于有关材料微观结构的物理思想和合理的假设，同时被设计用于有限元应用中的高效性和鲁棒性。通过大量实验数据的拟合表明，对于低变形和高应变，不同的变形状态和速率，保持时间和不同的温度，它几乎可以再现填充橡胶的全部现象。主要的建模范例是应力引起的微观结构分解和重组，它定义了材料随时间变化的行为，并允许再现对数弛豫效应。此外，在填料和交联剂含量变化的情况下，它的九个拟合参数以物理上合理的方式演变。推导了模型的静态极限情况，从而在必要时减少了参数数量并减少了计算量。最后，介绍了使用计算机生成的子例程进行的有限元实现，并针对扭转，径向，万向和轴向载荷下简化衬套的实验数据进行了测试。在填充剂和交联剂含量变化的情况下，它的九个拟合参数以物理上合理的方式演变。推导了模型的静态极限情况，从而在必要时减少了参数数量并减少了计算量。最后，介绍了使用计算机生成的子例程进行的有限元实现，并针对扭转，径向，万向和轴向载荷下简化衬套的实验数据进行了测试。在填料和交联剂含量变化的情况下，它的九个拟合参数以物理上合理的方式变化。推导了模型的静态极限情况，从而在必要时减少了参数数量和计算量。最后，介绍了使用计算机生成的子例程进行的有限元实现，并针对扭转，径向，万向和轴向载荷下简化衬套的实验数据进行了测试。