A deep material network for multiscale modeling of Viscoelastic-Viscoplastic porous structures with stochastic porosity level distribution

Structures that appear macroscopically homogeneous may nonetheless contain micrometric heterogeneities. One common source of such heterogeneity is the fabrication process. In selective laser sintering (SLS), for example, micro-pores are inherently formed, and their levels are spatially varying and randomly distributed. Capturing the effects of these micro-pores is challenging for most of the multiscale approaches, which are typically computationally prohibitive or suffer from accuracy loss. In this work, we propose an accurate and efficient multiscale modeling approach that addresses this problem. The proposed approach eliminates the computational burden of solving the lower scale problem, by substituting it with a graph-inspired network surrogate called the deep material network (DMN). During an offline phase, the DMN determines an accurate low-dimensional representation of the microstructure topology, which is then used instead of the full field one during the multiscale analysis. Here, our focus is on the interaction-based version of the DMN (IB-DMN), which we extended into two main directions. First, we incorporated the constitutive behavior of the thermoplastic polymer produced by SLS, which is coupled Viscoelastic-Viscoplastic (VE-VP). This behavior had not been previously studied in DMN context. Secondly, we developed the porosity guided DMN (Pg-DMN) to address stochastic distribution of void volume fraction. This relies on the construction of a limited set of base DMNs with known porosity levels, and inferring the behavior of each microstructure with new porosity level by interpolating between the base DMNs, without any additional training. The proposed surrogate is investigated under different loading conditions and across various strain rates against direct numerical simulation (DNS) and mean field homogenization (MFH). The results demonstrated strong generalization capabilities and substantial speedup at both microscopic and structural scales. This enabled to conduct accurate and efficient stochastic multiscale analyses of SLS printed structure which was previously out of reach. The strong potential of the approach for extension to other applications was illustrated with a VE-VP-ductile damage model implemented in a post-processing mode.