The linear viscoelastic behavior of materials is represented using mechanical models of choice, which are further utilized in different numerical investigations, such as finite element simulations and discrete element simulations. Burger's model is one of the widely adopted mechanical models and remains highly favored in contemporary research due to its multiple advantages. Specifically, it excels in representing long-term creep and stress relaxation behavior in a relatively simplified manner. Accurate identification of the long-term behavior for the viscoelastic material, particularly asphalt concrete, is crucial, as it serves as a key indicator of asphalt pavement performance over its service life. However, past research studies show that the parameters of Burger's model should be back-calculated from experimental data only within a limited range of frequency, otherwise, the parameters fail to represent the true material behavior. To the best of the authors’ knowledge, there is no approach for researchers to obtain the critical frequency range in which the experiments should be performed. Therefore, this study proposes a novel framework to find the critical frequency range to obtain appropriate model parameters of Burger's model, to better characterize the viscoelastic behavior of the materials. To examine the framework, asphalt concrete mixtures are used as examples in this study. Necessary laboratory tests including complex modulus tests and stress relaxation tests, are performed on two distinctive types of asphalt concrete mixtures. The generalized Maxwell model with different number of Maxwell chains are used to evaluate the performance of Burger's model. Furthermore, since commercially available finite element packages generally do not have a direct built-in Burger's model, the article shows a way of implementing Burger's model in finite element simulation. The simulations corresponding to the laboratory tests are carried out in both frequency domain and time domain to thoroughly evaluate the performance of Burger's model. The optimal frequency range of 0.1–20 Hz for the examined mixtures is found to significantly improve the accuracy of the descriptive master curve. The results also suggest that the generalized Maxwell model requires a minimum of four Maxwell chains to maintain good performance in accurately characterizing the behavior of asphalt mixtures. However, adding more Maxwell chains beyond a critical limit may not provide significant benefits. Finite element simulations demonstrate that the stress relaxation behavior predicted by the obtained Burger's model parameters aligns more closely with experimental data over longer time intervals. This makes Burger's model a strong choice for aiding in the design of simulations for studies focused on the long-term behavior of materials.

中文翻译：

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Burger 模型线性粘弹性表征的频率范围优化


材料的线性粘弹性行为使用所选的力学模型来表示，这些模型进一步用于不同的数值研究，例如有限元仿真和离散元仿真。Burger 模型是广泛采用的机械模型之一，由于其多重优势，在当代研究中仍然受到高度青睐。具体来说，它擅长以相对简化的方式表示长期蠕变和应力松弛行为。准确识别粘弹性材料（尤其是沥青混凝土）的长期行为至关重要，因为它是沥青路面在其使用寿命内性能的关键指标。然而，过去的研究表明，Burger 模型的参数应该只在有限的频率范围内从实验数据中进行反算，否则，这些参数无法代表真实的材料行为。据作者所知，研究人员没有办法获得应该进行实验的临界频率范围。因此，本研究提出了一种新的框架来找到临界频率范围，以获得 Burger 模型的适当模型参数，以更好地表征材料的粘弹性行为。为了检查框架，本研究以沥青混凝土混合物为例。对两种不同类型的沥青混凝土混合物进行必要的实验室测试，包括复模量测试和应力松弛测试。使用具有不同 Maxwell 链数的广义 Maxwell 模型来评估 Burger 模型的性能。 此外，由于市售的有限元包通常没有直接内置的 Burger 模型，因此本文介绍了一种在有限元仿真中实现 Burger 模型的方法。与实验室测试相对应的仿真在频域和时域中进行，以全面评估 Burger 模型的性能。发现所检查混合物的最佳频率范围 0.1-20 Hz 可显著提高描述性主曲线的准确性。结果还表明，广义 Maxwell 模型至少需要四个 Maxwell 链才能在准确表征沥青混合物的行为方面保持良好的性能。但是，添加超过 Critical Limit 的更多 Maxwell 链可能不会提供显着的好处。有限元仿真表明，由获得的 Burger 模型参数预测的应力松弛行为与较长时间间隔内的实验数据更紧密地一致。这使得 Burger 模型成为辅助设计仿真的有力选择，用于专注于材料长期行为的研究。