Prediction of elastic-plastic deformation of nanoporous metals by FEM beam modeling: A bottom-up approach from ligaments to real microstructures

Abstract

For the prediction of elastic-plastic deformation behavior of nanoporous materials, a computationally efficient method is needed that integrates the complex 3D network structure and the large variation of ligament shapes in a representative volume element. Finite element simulations based on beam elements are most efficient, but for a quantitative prediction, a correction is required that accounts for the effects of the mass around the junctions. To this end, a nodal correction is presented that covers a wide range of parabolic-spherical ligament shapes. Smooth functions are provided that define the extension of the nodal corrected elements along the ligament axis, their radius and their yield stress as functions of the individual ligament shape. It is shown that the increase in radius of the nodal beam elements can be replaced by scaled material parameters. Simulations of randomized FEM beam networks revealed that, in relation to the randomization of the ligament axis, the distribution of the ligament shape has a stronger impact on the macroscopic stress–strain response and should thus receive particular attention during the characterization of nanoporous microstructures. This also emphasizes the importance of the thickness analysis via image processing. Combining a nodal corrected FEM beam model with geometry data derived from image multiplication of the skeleton and Euclidean distance transform of a nanoporous gold FIB-SEM tomography dataset significantly improves the prediction of the stress–strain curve. The remaining deviation is expected to stem from the known underestimation of the real ligament diameter by the Euclidean distance transform as well as local variations in the circularity of the ligaments.