Time-space multiscale model for viscoelastic construction materials using the initial stress method.

Abstract

Viscoelastic materials such as polymer-modified asphalt, rubberized concrete, and structural adhesives are widely used in civil engineering for damping and deformation-recovery properties. However, their time-dependent and heterogeneous features hinder long-term performance prediction and structural integrity assessment, necessitating an efficient, accurate multiscale analysis. This study proposes a multiscale finite element method (MsFEM) for viscoelastic materials, integrating the generalized Maxwell model (GMM) and the initial stress method. It converts time-domain convolution constitutive relations into incremental elastic problems, retains a constant stiffness matrix to boost efficiency, and uses mesoscale heterogeneity-representing basis functions for coarse-fine mesh coupling. Validated via axial rod and cantilever beam examples, the method shows high accuracy against analytical solutions, serving as a robust tool for predicting material long-term performance with applications in structural health monitoring, life cycle assessment, and sustainable design.