A higher-order stress-resultant shell formulation based on multiscale homogenization

Paper in proceeding, 2009

In this paper, a multiscale method for simulating the mechanical response of a thin porous structure subjected to loading is proposed. Shell kinematics is adopted for the structure on the macroscopic scale while the stress resultants pertaining to the shell model are attained from the underlying porous microstructure via computational homogenization of the microscale quantities. The microstructural response is in its turn evaluated by solving a boundary value problem involving a Representative Volume Element (RVE) that extends through the full thickness of the porous structure. The resulting nested computational scheme accommodates that microscopic variations of deformation, i.e. the micro-fluctuations, are accounted for. This is necessary when it cannot be assumed that there is a separation between the spatial scale on which the deformation fields vary and the spatial scale of the microstructure. It can for example be the case for a thin foam layer included in a vehicle reinforcing component.