Filled rubbers are an important part of engineering materials because they have unique properties such as large deformability, increased stiffness and energy dissipation ability. The complexity of the material model parameter identification and the consideration of essential behaviours such as temperature dependence or residual strain may be a great challenge during the constitutive modelling. In this paper, a hyper-visco-pseudo-elastic constitutive equation is introduced and applied to model the complex behaviour of filled rubbers by considering (i) the Mullins effect, (ii) the temperature effect, and (iii) the effect of residual strains. The time-independent material response is provided by the modified Dorfmann–Ogden pseudo-elastic material model, while the time and temperature dependence is taken into consideration by the Prony series-based linear viscoelastic theory and the time-temperature superposition principle. Furthermore, by assuming homogeneous deformations, numerical stress solutions are presented to perform the material model calibration simple and fast, even when considering uniaxial tension/compression and simple shear simultaneously. The material model can be adapted to handle any hyperelastic model, arbitrary damage and residual strain variable, user-defined time-temperature superposition function, and any number of Maxwell elements (spring-dashpot terms). Here, the model parameters are determined from uniaxial stress relaxation-recovery tests, as well as cyclic uniaxial tensile and cyclic simple shear tests of different strain rates. Finally, the theoretical results are compared with experimental data for an EPDM rubber filled with 50 phr of carbon black.

填充橡胶是工程材料的重要组成部分，因为它们具有独特的性能，如大的变形能力、增加的刚度和能量耗散能力。材料模型参数识别的复杂性以及对温度依赖性或残余应变等基本行为的考虑可能是本构建模过程中的一大挑战。在本文中，通过考虑 (i) 穆林斯效应、(ii) 温度效应和 (iii) 残留的影响，引入了超粘滞伪弹性本构方程并将其应用于模拟填充橡胶的复杂行为。菌株。与时间无关的材料响应由改进的 Dorfmann-Ogden 伪弹性材料模型提供，而基于Prony级数的线性粘弹性理论和时间-温度叠加原理考虑了时间和温度的相关性。此外，通过假设均匀变形，即使同时考虑单轴拉伸/压缩和简单剪切，数值应力解也可以简单快速地执行材料模型校准。材料模型可适用于处理任何超弹性模型、任意损伤和残余应变变量、用户定义的时间-温度叠加函数以及任意数量的 Maxwell 单元（弹簧阻尼项）。在这里，模型参数由单轴应力松弛-恢复试验以及不同应变率的循环单轴拉伸和循环简单剪切试验确定。最后，