Abstract:
A three-dimensional finite element modeling for graphene nanocomposites usually requires very fine meshes. In case of plasticity, the computational efficiency of a micro representative volume element model is extremely low. For a remedy, based on the theory of nonuniform transformation field analysis, a reduced order homogenization method for graphene nanocomposites was proposed. First, we performed a pre-analysis for different loading paths to extract micro plastic strain fields; then a proper orthogonal decomposition of those field information was performed to obtain several plastic modes, which were used as basis functions for model order reduction. A constitutive model of reduced variables was derived from the equivalence of macro and micro dissipation power. The offline analysis of this method was implemented in MATLAB. For engineering computations, the online analysis was implemented by the user subroutine interface UMAT of the commercial finite element software ABAQUS. The effectiveness of the proposed method was illustrated by three-dimensional numerical examples. The results show that the acceleration rate for 3D representative volume element computations is of the order of 10
3~10
4, while maintaining a sufficient accuracy level.