Uncured styrene-butadiene rubber (SBR) can be modelled as a viscoelastic material with at least two different relaxation mechanisms. In this paper we compare multi-mode constitutive models combining two viscoelastic modes (linear and/or nonlinear) in three possible ways. Our particular choice of the two modes was inspired by models originally developed to describe the response of asphalt binders. We select the model that best fits the experimental data obtained from a modified stress relaxation experiment in the torsional configuration of the plate–plate rheometer. The optimisation of the five model parameters for each model is achieved by minimising the weighted least-squares distance between experimental observations and the computer model output using a tree-structured Parzen estimator algorithm to find an initial guess, followed by further optimisation using the Nelder–Mead simplex algorithm. The results show that the model combining the linear mode and the nonlinear mode is the most suitable variant to describe the observed behaviour of SBR in the given regime. The predictive capabilities of the three models are further examined in changed experimental and numerical configurations. Full data and code to produce the figures in this article are included as supplementary material.

可以将未固化的丁苯橡胶（SBR）建模为具有至少两种不同松弛机制的粘弹性材料。在本文中，我们以三种可能的方式比较了结合两种粘弹性模式（线性和/或非线性）的多模式本构模型。我们对这两种模式的特别选择是受最初开发用来描述沥青粘合剂反应的模型的启发。我们选择最适合在板-板流变仪的扭转配置中从修改后的应力松弛实验获得的实验数据的模型。每个模型的五个模型参数的优化是通过使用树状结构的Parzen估计器算法找到初始猜测，以最小化实验观测值与计算机模型输出之间的加权最小二乘方距离来实现的，然后使用Nelder-Mead单纯形算法进行进一步优化。结果表明，将线性模式和非线性模式相结合的模型是描述给定状态下SBR观察到的行为的最合适变体。在变化的实验和数值配置中，进一步检查了这三个模型的预测能力。包含本文中产生图的完整数据和代码作为补充材料。