A three-scale asymptotic analysis for ageing linear viscoelastic problems of composites with multiple configurations

A novel three-scale asymptotic expansion is proposed in this work to investigate ageing linear viscoelastic problems of composites with multiple periodic configurations. Here, the composite structures are established by periodical distribution of local cells on microscale and mesoscale. The new three-scale asymptotic expansion formulas based on classical homogenized methods in time domain are constructed at first, and the microscale and mesoscale functions are also derived in detail. Further, two distinct homogenized parameters defined on microscale and mesoscale domains are obtained by upscaling methods, and the newly developed homogenized equations are given on whole structure in time domain. Then, the three-scale strain and stress solutions are constructed by assembling the unit cell solutions and homogenized solutions. Also, the efficient finite element algorithms based on the three-scale asymptotic expansion and homogenized method are brought forward. Finally, some representative numerical examples are evaluated to verify the proposed methods. They show that the three-scale asymptotic expansions developed in this work are effective and valid for predicting the ageing linear viscoelastic properties of the composite materials with multiple configurations.