The Huet-Sayegh (HS) and 2S2P1D rheological models represent very well the linear viscoelastic behaviour of asphalt concrete and binder while using less parameters than other models. However, the finite element implementation in time domain of these two models encounters a great difficulty. In this paper, the author aims at developing a numerical implementation in time domain of the HS and 2S2P1D models. Firstly, the relaxation modulus is analytically approximated using Schapery and Park’s method or exactly calculated using the numerical algorithm proposed by Heck. Secondly, the relaxation modulus is once again approximated by the sum of exponential functions for deriving a recursive formula of stress–strain relationship. Since the relaxation modulus is approximated twice, a special technique is used to estimate the appropriate decay rates and coefficients of the sum of exponential functions to ensure high accuracy of the obtained results. It is shown that the calculations based on the proposed formulation achieve a very good level of accuracy.

Huet-Sayegh (HS) 和 2S2P1D 流变模型很好地代表了沥青混凝土和粘合剂的线性粘弹性行为，同时使用的参数比其他模型少。然而，这两种模型在时域的有限元实现都遇到了很大的困难。在本文中，作者旨在开发 HS 和 2S2P1D 模型时域中的数值实现。首先，松弛模量使用 Schapery 和 Park 的方法在解析上近似或使用 Heck 提出的数值算法精确计算。其次，松弛模量再次由指数函数的总和来近似，以推导出应力-应变关系的递归公式。由于松弛模量近似为两倍，使用一种特殊的技术来估计适当的衰减率和指数函数和的系数，以确保获得的结果具有较高的准确性。结果表明，基于所提出的公式的计算达到了非常好的准确度。