Multiscale homogenization and localization of materials with hierarchical porous microstructures

摘要

Using an efficient, elasticity-based homogenization theory, we investigated the effect of porosity redistribution at different microstructural scales on the homogenized moduli and local stress fields of periodic materials with hierarchical porosities. A recursive algorithm was developed wherein homogenized moduli and local stress fields obtained from the homogenization and localization analysis at one scale are used in the calculation of homogenized moduli at the next scale. This recursive algorithm is employed until the largest scale is reached. We illustrate the developed computational capability for a two-scale periodic material by generating homogenized moduli and stress concentrations during the process of porosity redistribution between the scales. Results of extensive parametric studies, enabled by the elasticity-based hierarchical homogenization algorithm, show that largest homogenized moduli and lowest stress concentration may be obtained through proper choice of relevant parameters. The algorithm is also applicable to hierarchical materials with nanoscale porosities with surface-elasticity effects taken into account using the Gurtin-Murdoch model. Coupling the integrated homogenization/localization framework with the Particle Swarm Optimization facilitates direct identification of multiscale porous microstructures with the lowest stress concentration for a given targeted homogenized modulus, verified upon comparison with the parametric study results. The present work provides guidelines for the design of multiscale porous materials.