ABSTRACT of the Doctoral Thesis

This work shows the development of a the finite element based two-scale
analysis method to study problems related to the mechanical behavior of
inhomogeneous materials under monotone static loading conditions, as well as,
their experimental investigation.
The inhomogeneities, which influence the effective mechanical response by
their topology, geometry and material behavior, can occur on different length
scales.
In the case of perforated (acoustic) laminates, which are studied in this work,
the following inhomogeneities are evident on the different length scales:

- Macro-scale: ... periodically arranged holes (perforations)

- Meso-scale: ... different laminae (plies)

- Micro-scale: ... fiber and matrix material

- ...

In the current case the modeling goes down to the meso-scale and is realized
by unit cell models and hierarchical meso-macro (two-scale) concepts.

Perforated laminates are applied, e.g., as face sheets in sandwich compounds in the casing of aircraft turbine engines. They are designed for absorbing noise and, in the most cases, they must carry mechanical loads as well. Hence, the effective stiffness behavior, the local stress distribution in the individual layers, and the effective strength of the perforated laminate are of interest.

For calculating the effective stiffness behavior of perforated laminates the homogenization method is applied. Homogenization means that the actual inhomogeneous material (e.g., the perforated composite) is replaced by an equivalent homogeneous material, with the calculated homogenized stiffness leading to the same macroscopic deformation behavior.

The described failure investigations are based on linear 3D finite element unit cell calculations, where inter-laminar stresses (due to free edge effects) are taken into account. Numerous failure models have been developed for strength predictions in perforated laminates. In this work a stress based failure model, the average stress model, is used. In this model averaged stresses (instead of true stresses around the hole) are used in combination with first ply failure (FPF) strength values, as input for different 3D failure criteria. Applied failure criteria are: The Tsai-Wu criterion, the maximum stress criterion, the new Puck criterion, and a delamination criterion. The goal of the failure analysis is to calculate a safety factor or risk parameter for all possible in-plane loading combinations. The results of these computations are failure-initiation surfaces in the space of macro-membrane forces.

The deformation and strength evaluation of structures, which contain such perforated laminates, can be performed simply and fast on the structural level (macroscopic level) by using the effective stiffness and the failure-initiation surfaces. Furthermore, the structural analysis does not need to account explicitly for the perforations, neither in the finite element discretization nor in the evaluation of stress fields. Finally the introduced numerical models are verified by experiments. Tensile tests on perforated and non-perforated laminates are performed in combination with acoustic emission measurements to obtain the first ply failure strengths of the perforated and non-perforated laminate. The obtained test results shows good agreement with the numerical predictions.

revised 030410 (hjb)