Multiscale modelling of porous polymers using a combined finite element and D-optimal design of experiment approach

This paper presents a general numerical procedure for the analysis of polymeric materials containing spherical voids. The multiscale approach implemented simulates, via three dimensional finite-element analysis, an infinite medium of the material containing discrete voids. A D-optimal design procedure is used to combine the seven normalized variables considered in the problem: the material strength and ductility, the hardening ratio, the void volume fraction, the void arrangement (number of voids), the stress triaxiality and the Lode parameter. The failure criterion considered is based on a critical distance approach, considering a brittle epoxy resin as a reference material. Results are provided for the normalized equivalent stress and strain at failure, the void growth rate and the equivalent failure strain. The influence of the variables on the outputs is estimated and design equation coefficients are calculated.