ON MICRO/MESO/MACRO MODELING OF COMPOSITE LIGHTWEIGHT MATERIALS AND STRUCTURES

Abstract

The effective, i.e. overall mechanical response of multi-phase or other microstructured materials is influenced by the topology and the geometry of the individual phases as well as by the mechanical behavior of the material and interface at lower length scales, i.e. meso-, micro- and submicroscales. The present contribution shows examples for the application of finite element methods to study problems related to the mechanical behavior of inhomogeneous materials by unit cell models and hierarchical micro-meso-macro concepts. After basic considerations of the formulation of proper unit cells and corresponding homogenization procedures, some typical applications to highly porous metals (metal foams) and composites are discussed. The main body of the paper deals with the calculation of the stiffness and the failure behavior of perforated composite laminates, used as so-called acoustic skins for sound absorbing components in airplane structures. Based on the above mentioned unit cell concepts effective stiffness properties as well as a macroscopic failure-initiation surface in the space of macro-membrane forces is determined for the use in structural analyses. Both inter- and intra-laminar failure as well as free edge effects are taken into account on the meso-level. In this way the deformation and strength evaluation of structures containing such perforated laminates can be performed simply on the structural, i.e. macroscopic level. This procedure is very efficient: the structural analysis does not need to account for of the perforation, neither in the finite element discretization nor in the evaluation of local stress fields.