An anisotropic damage model of foams on the basis of a micromechanical description

Abstract

The mechanical behavior of open-cell foams may be modeled either on a microscopic or a macroscopic scale. In the first case, the behavior of the individual cell walls is described by beam models, while in the second case a continuum mechanical approach is applied. Both approaches have different advantages: On the one hand, the microscopic approach allows for a simple formulation of the constitutive equations but requires detailed knowledge of the heterogeneous microstructure, e.g. geometrical data of the beams and of the topology, and becomes numerically expensive for large structures. On the other hand, the macroscopic approach leads to efficient computations but requires more complicated constitutive equations, if e.g. anisotropy is taken into account.

In the present contribution the advantages of the microscopic and macroscopic descriptions are combined by a numerical so-called second order homogenization scheme. Therefore, a small but representative element of the microstructure consisting of a few beam elements is chosen and attached to the quadrature points of the macroscopic finite element model. The macroscopic model is formulated in the framework of a Cosserat continuum, which allows to take care of size effects. The macroscopic strain and curvature tensors are projected onto the microstructure leading to a deformation mode of the beam ensemble. The resulting forces and moments in the beams are homogenized by an appropriate averaging procedure defining the corresponding stresses and couple stresses on the macroscale. In this approach, anisotropy is included in a natural way choosing an anisotropic distribution of the beams in the testing volume element (TVE). In addition, damage is described on the microscopic level of the individual beams.