Abstract Reliable numerical modeling of asphalt concrete (AC) is a complex problem due to a non periodic random structure of this material and a nonlinear behavior of its interacting constituents. Phenomena observed at the lower resolution highly influence the overall response of pavement layers made of asphalt concrete. In this paper, we focus on the selected aspects of its efficient numerical modeling using the viscoelastic Burgers material model. In this paper, we focus on two important components of the modeling process. Firstly, we present a straightforward algorithm for the random AC structure generation, which is automatically linked with the finite element (FE) mesh generation. It is based on the predefined shapes of inclusions and the relocation of nodes of the regular grid. Such an approach provides definitely coarser (but related to the microstructure) FE meshes than other ones used for this purposes. Thus, it saves a lot of computer resources at this level of the modeling process. Our next development concerns further reduction of the number of degrees of freedom (NDOF) that are necessary to tackle the heterogeneous domain. We take advantage of the multiscale finite element method (MsFEM) to solve given problems using a coarse macroscale mesh. Within its elements, we construct special shape functions of order 1, 2 or 3 revealing the complexity of the microresolution. We propose a novel extension of the linear elastic analysis to the viscoelastic one in terms of the MsFEM. Combining the aforementioned approaches, we provide a versatile tool for the numerical modeling of asphalt concrete. The proposed framework is illustrated with the examples of the special shape function constructions and the solutions to the compression tests of the samples made of AC. Obtained results confirm the efficiency and applicability of the proposed methodology.

中文翻译：

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基于多尺度有限元法的沥青混凝土建模

摘要 沥青混凝土 (AC) 的可靠数值模拟是一个复杂的问题，因为这种材料的非周期性随机结构及其相互作用成分的非线性行为。在较低分辨率下观察到的现象极大地影响了沥青混凝土路面层的整体响应。在本文中，我们使用粘弹性 Burgers 材料模型关注其有效数值建模的选定方面。在本文中，我们关注建模过程的两个重要组成部分。首先，我们提出了一种用于随机 AC 结构生成的简单算法，该算法与有限元 (FE) 网格生成自动链接。它基于预定义的夹杂物形状和规则网格节点的重新定位。与用于此目的的其他方法相比，这种方法提供的有限元网格肯定更粗糙（但与微观结构相关）。因此，它在建模过程的这个层次上节省了大量的计算机资源。我们的下一个发展涉及进一步减少解决异构域所需的自由度 (NDOF) 的数量。我们利用多尺度有限元方法 (MsFEM) 来解决使用粗宏观尺度网格的给定问题。在其元素中，我们构建了 1、2 或 3 阶的特殊形状函数，揭示了微分辨率的复杂性。我们建议根据 MsFEM 将线弹性分析扩展到粘弹性分析。结合上述方法，我们提供了一种用于沥青混凝土数值建模的通用工具。所提出的框架通过特殊形状函数构造的示例和由 AC 制成的样品的压缩测试的解决方案来说明。获得的结果证实了所提出方法的效率和适用性。