Numerical prediction of effective properties for heterogeneous viscoelastic materials via a temporally recursive adaptive quadtree SBFEM

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.