Direct FE2 for concurrent multilevel modeling of heterogeneous thin plate structures

The FE 2 method systematically translates macro kinematic constraints to the underlying (micro) RVEs and extracts the effective RVE responses to macro continuum in an energetically consistent manner. In the literature, many researchers have demonstrated the predictive capability of FE 2 across a wide range of problems. The conventional FE 2 numerical framework adopts a staggered solution strategy between the macro and micro analyses. This limits the adoption of FE 2 method by inexperienced researchers/ engineers to solve practical engineering problems using commercial FE software. To this end, a Direct FE 2 method has been proposed in Tan et al. (2020) and implemented in the commercial software ABAQUS, where macro kinematic constraints are applied directly on the RVEs superimposed on the macro elements. This results in a monolithic numerical framework, without the need to write any subroutines. Compared to the conventional FE 2 implementation using commercial software, the number of floating-point operations is also reduced because the nested FE calculations are condensed into one in Direct FE 2 (Raju et al., 2021). In this contribution focusing on thin plate structures, the Direct FE 2 method is extended based on Kirchhoff–Love thin plate kinematics and implemented in ABAQUS without the need for subroutines. The performance of the Direct FE 2 method for this higher order formulation is demonstrated by comparing against reference solutions from direct numerical simulations . Sample files can be downloaded from https://github.com/leonghien/Direct-FE2-thin-plates.git . • Extension of Direct FE 2 method for thin plate structures, leading to a plate continuum at macro scale. • Direct implementation of computational homogenization in ABAQUS without requiring any subroutines. • Good results demonstrated for reinforced concrete slabs compared against direct numerical simulations.