A novel recursive-cluster based reduced order method is presented to predict the effective properties of heterogeneous viscoelastic materials. By virtue of a piecewise series expansion based variable separation, a temporally and spatially homogenization process is decoupled into a series of recursive elastic homogenization ones, which require only one-time clustering decomposition with one-time elastic heterogeneous analysis. Such that, the heavy computational burden caused by the direct numerical simulation over the whole domain of viscoelastic heterogeneous RUC can significantly be alleviated. The effective creep compliance or relaxation modulus is presented via a time varying average strain or average stress, and a piecewise adaptive technique is proposed to secure the temporal accuracy when step size varies. Numerical examples are provided to demonstrate the effectiveness and efficiency of proposed approach, and the predicted results agree well with those given by FEM/SBFEM based viscoelastic DNS.

提出了一种新颖的基于递归聚类的降阶方法来预测异质粘弹性材料的有效性能。通过基于分段级数展开的变量分离，时间和空间均质化过程被解耦为一系列递归弹性均质化过程，这些过程只需要一次聚类分解和一次弹性异构分析。这样，可以显着减轻粘弹性异质 RUC 整个域的直接数值模拟所带来的繁重计算负担。有效蠕变柔量或松弛模量通过时变平均应变或平均应力表示，并提出分段自适应技术以确保步长变化时的时间精度。