An alternative modelling framework is proposed for capturing the rate-dependency in the loading and unloading (i.e., with softening) deformation behaviour of a wide range of isotropic incompressible elastomers. The proposed framework departs from the existing approaches in the literature which assume an additive contribution of the ‘non-equilibrium’, or ‘viscous’, part to the elastic response. Instead, here it is considered that the model parameters of the basic hyperelastic function evolve (i.e., vary) with the deformation rate. That is, the basic hyperelastic model parameters are considered as functions of rate, given the deformation rate as a parameter and not a variable, pre-set in experiments. While the nature, and choice, of this functional dependency is empirical, a simple linear relationship is considered in this work between the parameters of a chosen basic hyperelastic model and the applied deformation rate. Using this specialisation, the model is applied to extant experimental data of a variety of elastomers including 3D-printed elastomeric polyurethane (EPU), dielectric elastomer VHB 4910, commercial 3D-printed silicone (SIL30) and filled rubber Viton™ specimens under uniaxial loading – unloading deformations at various rates. It is shown that the model favourably captures the considered datasets. The mathematical simplicity of the proposed modelling framework, comparatively lower number of model parameters, and the favourable modelling and predictive results suggest that the implementation and application of this modelling framework is efficient and tractable, and merit further consideration for modelling the rate-dependant mechanical behaviour of a wider range of rubber-like materials and loading modalities.

提出了一种替代建模框架，用于捕获各种各向同性不可压缩弹性体的加载和卸载（即软化）变形行为的速率依赖性。所提出的框架不同于文献中的现有方法，文献中假设“非平衡”或“粘性”部分对弹性响应的附加贡献。相反，这里认为基本超弹性函数的模型参数随变形率演化（即变化） 。也就是说，基本超弹性模型参数被视为速率的函数，将变形率作为参数而不是一个变量，在实验中预先设定。虽然这种函数依赖性的性质和选择是经验性的，但本工作考虑了所选基本超弹性模型的参数与所应用的变形率之间的简单线性关系。利用这一专业知识，该模型适用于各种弹性体的现有实验数据，包括单轴载荷下的 3D 打印弹性体聚氨酯 (EPU)、介电弹性体 VHB 4910、商用 3D 打印硅胶 (SIL30) 和填充橡胶 Viton™ 样本 –以不同的速率卸载变形。结果表明，该模型可以很好地捕获所考虑的数据集。所提出的建模框架的数学简单性，模型参数数量相对较少，