High-order three-scale method for mechanical behavior analysis of composite structures with multiple periodic configurations

A new high-order three-scale (HOTS) method for simulating the mechanical behaviors of composite material structures with multiple heterogeneities is developed. The heterogeneities of the structures are taken into account by periodic layouts of unit cells on the microscale and mesoscale. A novel unified micro-meso-macro multiscale formulation based on reiterated homogenization and multiscale asymptotic expansions is established successively. Two kinds of local cell functions defined on the mesoscale and microscale cells, including first- and second-order, are established. The equivalent material parameter is calculated by up-scaling procedure and homogenized problem is subsequently defined. Further, the displacement, strain and stress are constructed as multiscale asymptotic expansions by assembling the cell functions and homogenation solution. In the present method, both the mesoscopic and microscopic information are synthesized with homogenization solution to capture more local characteristics inside the composite material structures. Then, the finite element numerical algorithm based on the three-scale method is brought forward in details. Finally, numerical examples are given to demonstrate the usability of the HOTS analysis method to simulate the mechanical behavior. This study offers a unified multiscale framework that enables mechanical behavior analysis of composite structures with multiple spatial scales.