Abstract A new numerical method is presented for evaluating the effective properties of heterogeneous viscoelastic materials, and an efficient and high-fidelity Direct Numerical Simulation (DNS) is addressed by integrating the advantages of the quadtree Scaled Boundary Finite Element Method (SBFEM) and a temporally recursive adaptive algorithm. The quadtree technique that can be directly implemented with input images is utilized for the mesh generation of the Representative Volume Element (RVE) with complex constitutes, and the inconvenience caused by ‘hanging nodes’ and the interface conformity requirement in the mesh generation can be removed using a polygonal Scaled Boundary Finite Element (SBFE). The computing accuracy in the time domain can be stably achieved via a recursive adaptive process when the step sizes vary. By virtue of the proposed DNS, an inverse analysis based procedure is designed to estimate the effective viscoelastic properties, and two indicators are proposed to evaluate the effectiveness of estimation. Numerical verification is provided to demonstrate the effectiveness of the proposed approach, and the impacts of the distributions and shapes of inclusions, RVE sizes, and volume fractions are taken into account.

中文翻译：

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通过时间递归自适应四叉树 SBFEM 对异质粘弹性材料的有效性能进行数值预测

摘要 提出了一种评估异质粘弹性材料有效性能的新数值方法，并结合四叉树标度边界有限元法 (SBFEM) 和时间有限元法的优点，实现了高效、高保真直接数值模拟 (DNS)。递归自适应算法。利用输入图像可以直接实现的四叉树技术对具有复杂结构的代表性体积元（RVE）进行网格生成，消除了网格生成中“悬点”和界面一致性要求带来的不便使用多边形缩放边界有限元 (SBFE)。当步长变化时，通过递归自适应过程可以稳定地达到时域的计算精度。凭借所提出的 DNS，设计了一个基于逆分析的程序来估计有效粘弹性，并提出了两个指标来评估估计的有效性。提供了数值验证来证明所提出方法的有效性，并考虑了夹杂物的分布和形状、RVE 尺寸和体积分数的影响。