A recursive-cluster based reduced order method for numerical prediction of effective properties of heterogeneous viscoelastic materials

Abstract

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. • Propose a recursive-cluster based reduced order method to evaluate effective properties of heterogeneous viscoelastic materials. • Decouple a temporally and spatially homogenization process into a series of recursive elastic homogenization ones. • Take only one-time clustering decomposition with one-time elastic heterogeneous analysis. • Execute a piecewise adaptive computing to gain the effective strains of clusters on RUC. • Circumvent the heavy computational burden caused by the high-fidelity viscoelastic DNS on RUC significantly.