We address the calculation of the effective properties of non-aging linear viscoelastic composite materials. This is done by solving the microscale periodic local problems obtained via the Asymptotic Homogenization Method (AHM) by means of finite element three-dimensional simulations. The work comprises the investigation of the effective creep and relaxation behavior for a variety of fiber and inclusion reinforced structures (e.g. polymeric matrix composites). As starting point, we consider the elastic-viscoelastic correspondence principle and the Laplace-Carson transform. Then, a classical asymptotic homogenization approach for composites with discontinuous material properties and perfect contact at the interface between the constituents is performed. In particular, we reach to the stress jump conditions from local problems and obtain the corresponding interface loads. Furthermore, we solve numerically the local problems in the Laplace-Carson domain, and compute the effective coefficients. Moreover, the inversion to the original temporal space is also carried out. Finally, we compare our results with those obtained from different homogenization approaches, such as the Finite-Volume Direct Averaging Micromechanics (FVDAM) and the Locally Exact Homogenization Theory (LEHT).

我们着眼于非老化线性粘弹性复合材料的有效性能计算。这是通过有限元三维模拟解决通过渐近均质化方法（AHM）获得的微观周期性局部问题来完成的。这项工作包括研究各种纤维和包裹体增强结构（例如聚合物基复合材料）的有效蠕变和松弛行为。作为起点，我们考虑了弹性-粘弹性对应原理和Laplace-Carson变换。然后，对具有不连续材料特性且在组分之间的界面处完美接触的复合材料执行经典渐近均质化方法。尤其是，我们从局部问题得出应力跃变条件，并获得相应的界面载荷。此外，我们在数值上解决了Laplace-Carson域中的局部问题，并计算了有效系数。此外，还进行了到原始时间空间的反转。最后，我们将我们的结果与从不同均质化方法获得的结果进行比较，例如有限体积直接平均微力学（FVDAM）和局部精确均质化理论（LEHT）。