Computational homogenization of 3D printed materials by a reduced order model

The aim of this paper is to study the effective mechanical behavior of 3D printed materials. To this purpose a micromechanical study is developed in order to investigate the influence of the heterogeneity of the 3D printed material at the microscale on the overall response. A reduced order model, usually adopted for the analysis of heterogeneous materials, is extended to model the response of the printed material, considered as periodic. In particular, the Mixed Transformation Field Analysis (MxTFA), based on a mixed-stress variational formulation of the elasto-plastic theory, considering the inelastic strain based on a representation of the self-equilibrated stresses, is developed. A unit cell, representative of the 3D printed material's microstructure, comprising a fiber and interstitial voids is defined and divided in subsets. In each subset, a self-equilibrated stress is considered introducing a constant, linear, or quadratic approximation and the plastic multiplier is assumed constant. Some numerical applications are developed considering different unit cells and different loading conditions. The obtained results are compared with some experimental results, available in literature, and with results obtained from non-linear finite element analyses. The application of a TFA-based method to the 3D printed materials could provide an effective tool for the prediction of the mechanical behavior with a significant reduction of the history variables defining the evolution problem.