Rubberlike materials exhibit strong rate-dependent mechanical response which manifests itself in creep and relaxation tests as well as in the hysteresis curves under cyclic loading. Unlike linear viscoelasticity, creep and relaxation response of rubber is nonlinear and amplitude-dependent. Within this context, the contribution of this work is three fold. (i) On the experimental side, the characterization of equilibrium and non-equilibrium responses are carried out by means of uniaxial and equibiaxial extension tests. Also performed are the creep and relaxation experiments at various stress and strain levels. (ii) On the theoretical side, we extend the well-known eight-chain model via incorporating a simple yet instrumental tube-constraint term composed of the second invariant into the non-affine network contribution reflecting the ground state equilibrium response. For the non-equilibrium response, we propose a new evolution equation for the creep/relaxation behavior of rubberlike materials based on a relaxation kinetics of a single polymer chain. The geometric non-linearity is incorporated via the finite deformation kinematics based on the multiplicative split of the deformation gradient into elastic and viscous parts, whereas the volumetric and isochoric split of the deformation gradient is entirely discarded. The rheology uses a nonlinear spring responsible for equilibrium elastic response in parallel to n number of Maxwell elements, leading to a generalized Maxwell-Wiechert viscoelastic solid. (iii) The algorithmic implementation of the model features the spectral decomposition of the respective terms and is demonstrated within the context of the finite element method. The developed model is validated by fitting both the elastic and viscoelastic model responses with respect to the experimental data in the sense of uniaxial, (equi)biaxial extensions, and pure shear tests. Relaxation and creep behavior of the model are thoroughly assessed. Also presented in the manuscript is the capability and the performance of the model in the face of a relevant non-homogeneous boundary value problem. The quality of the findings earns the model vast utilization areas from an engineering perspective.

橡胶状材料表现出很强的速率依赖性机械响应，这在蠕变和松弛测试以及循环载荷下的磁滞曲线中均表现出来。与线性粘弹性不同，橡胶的蠕变和松弛响应是非线性的，并且与振幅有关。在这种情况下，这项工作的贡献是三方面的。（i）在实验方面，通过单轴和等双轴延伸试验对平衡和非平衡响应进行表征。还进行了在各种应力​​和应变水平下的蠕变和松弛实验。（ii）从理论上讲，我们通过合并一个简单但有用的管约束项来扩展著名的八链模型由第二个不变量组成的非仿射网络贡献反映了基态的平衡响应。对于非平衡响应，我们基于单个聚合物链的松弛动力学，为橡胶状材料的蠕变/松弛行为提出了一个新的演化方程。通过基于变形梯度的乘性分裂的有限变形运动学，将几何非线性纳入弹性和粘性部分，而完全忽略了变形梯度的体积和等分分裂。流变学使用非线性弹簧负责与n平行的平衡弹性响应Maxwell元素的数量，从而生成广义的Maxwell-Wiechert粘弹性固体。（iii）该模型的算法实现以各个项的频谱分解为特征，并在有限元方法的上下文中得到证明。通过对单轴，（等）双轴延伸和纯剪切试验意义上的实验数据拟合弹性和粘弹性模型响应，可以验证所开发的模型的有效性。彻底评估了模型的松弛和蠕变行为。在手稿中还介绍了面对相关非均匀边界值问题时模型的功能和性能。从工程的角度来看，发现的质量为模型赢得了广泛的应用领域。