Homogenization and localization of elastic-plastic nanoporous materials with Gurtin-Murdoch interfaces: An assessment of computational approaches

Abstract

This paper critically examines the predictive capabilities of three computational approaches for the elastic-plastic response of nanoporous materials with energetic surfaces simulated with the Gurtin-Murdoch coherent interface model. These approaches involve the classical composite cylinder assemblage model, and the finite-element and generalized finite-volume homogenization theories. Exact elastic-plastic solution to the composite cylinder assemblage under axisymmetric loading is obtained analytically such that all the governing differential equations are satisfied exactly. Hence it is used as gold standard in assessing the predictive capability of the newly developed generalized finite-volume theory with surface and plasticity effects, as well as a comparable finite-element approach, under axisymmetric loading and porosity volume fractions for which pore interactions are small. The assessment includes homogenized response and local stress and plastic strain fields, as well as solution stability issues for surfaces with negative strain energies that limit the range of pore radii and volume fractions of nanoporous materials that may be analyzed. The effect of surface elasticity is shown to be magnified in the elastic-plastic region. Anomalous homogenized response that results from the use of the elastic Gurtin-Murdoch model which impacts limit surface calculations is highlighted. The generalized finite-volume theory is shown to exhibit larger range of pore radii relative to the finite-element based homogenization wherein stable solutions are obtained under both axisymmetric and asymmetric loading of hexagonal and square arrays of porosities with negative strain energies.