The simulation of 3D fatigue crack growth is investigated and in combination with suitable experiments it is aimed to identify a reliable crack growth criterion. To perform the crack growth simulation as effectively as possible the boundary element method (BEM) in terms of the 3D Dual BEM is utilized. The relevant boundary integral equations are evaluated in the framework of a collocation procedure. To compress the system matrix and to speed-up the solution procedure the adaptive cross approximation (ACA) method is applied. It is an algebraic technique acting purely on the system matrix itself. The efficiency of this procedure with respect to crack problems will be shown on both a standard fracture specimen and an industrial application.
Abstract-The on-going reduction of the on-chip feature size goes together with an increase of process variability. While the manufacturer is expected to improve the uniformity of its output, and the designers are expected to enhance circuit adaptability and reliability, the design tools are expected to deliver convenient and fast approaches capable of giving accurate characterizations of manufacturing tolerances. In this paper, we present an algorithm that enables an extension of 3-D capacitance extractors to generate both the nominal capacitances and their sensitivities w.r.t. all geometric parameters with only one extraction. Using the domaindecomposition technique, it is shown that sensitivities can be derived from the intermediate data of the standard capacitance extraction using the Boundary Element Method (BEM). The algorithm has been implemented in a layout-to-circuit extractor. It is shown by experiments that the additional cost for the sensitivity computation is less than 20% of the standard time consumption, essentially independent of the number of parameters.
An advanced incremental crack growth algorithm for the three-dimensional (3D) simulation of fatigue crack growth in complex 3D structures with linear elastic material behavior is presented. To perform the crack growth simulation as effectively as possible an accurate stress analysis is done by the boundaryelement method (BEM) in terms of the 3D dual BEM. The question concerning a reliable 3D crack growth criterion is answered based on experimental observations. All criteria under consideration are numerically realized by a predictor-corrector procedure. The agreement between numerically determined and experimentally observed crack fronts will be shown on both fracture specimens and an industrial application.
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