Direct FE2 modeling of heterogeneous materials with a micromorphic computational homogenization framework

Direct FE 2 , recently proposed by Tan et al. (2020), is a concurrent multilevel modeling approach, which homogenizes a representative volume element (RVE) to a Cauchy continuum but calls for only a single finite element analysis . In this paper, the method is extended to homogenization towards a micromorphic continuum. It allows us to capture the deformation of composites with soft inclusions in the absence of scale separation and the size effects therein. Besides the displacement field, additional morphic fields are employed at the macroscale to characterize the micro-scale heterogeneity. Compared with the classical FE 2 approach, the only effort in the development of the Direct FE 2 is to formulate the macro–micro transition as kinematic constraints between the macro and micro DOFs, that are implemented through multi-point constraints (MPC) in Abaqus®. Automatically, the MPCs enable the micro–macro transition in an energetically consistent way and correlate the microscopic traction back to the macroscopic nodal internal force. The performance of the novel Direct FE 2 modeling is benchmarked with three representative numerical simulations, where a better predictive capability than the classical one is demonstrated in situations without a clear separation of scales.