A hybrid direct FE2 method for modeling of multiscale materials and structures with strain localization

Abstract

Strain localization is a common phenomenon existing in various multiscale materials or structures, e.g., the bulking bands of thin-walled structures, the local collapse of porous materials, and the crack in solid materials, etc. However, this phenomenon cannot be captured by the conventional homogenization methods, such as mean-field homogenization (e.g., Mori–Tanaka method), first-order or high-order computational homogenization (e.g., the Finite Element Square method), etc., due to the high strain gradient associated with strain localization. Aiming at this, a hybrid Direct FE2 method is proposed by combining the D-FE2 (Direct FE2) and the traditional FE methods, while the multiscale structure is modeled using the D-FE2 method in the region exhibiting low deformation gradient, and the other region displaying high deformation gradient is modeled using the traditional FE method. Moreover, a node displacement constraint and an overall node displacement constraint derived from the multilevel equilibrium equations using the Gauss–Ostrogradsky theorem are respectively prescribed to the interface between the D-FE2 model and the FE model of the multiscale structure, to enforce the energy equilibrium and deformation continuity. The proposed hybrid D-FE2 method is then applied to predict the strain localization behavior of multiscale materials or structures, including local bulking of honeycomb structures, in-situ crack propagation, and localized plastic deformation in fiber reinforced composites, etc. Comparison of the simulation results obtained from the hybrid D-FE2 method and the traditional FE method validates the accuracy, efficiency and ease of numerical implementation of the proposed hybrid D-FE2 method.