We present an algorithm which produces a decomposition of a regular cellular
complex with a discrete Morse function analogous to the Morse-Smale
decomposition of a smooth manifold with respect to a smooth Morse function. The
advantage of our algorithm compared to similar existing results is that it
works, at least theoretically, in any dimension. Practically, there are
dimensional restrictions due to the size of cellular complexes of higher
dimensions, though. We prove that the algorithm is correct in the sense that it
always produces a decomposition into descending and ascending regions of the
critical cells in a finite number of steps, and that, after a finite number of
subdivisions, all the regions are topological discs. The efficiency of the
algorithm is discussed and its performance on several examples is demonstrated.Comment: 23 pages, 12 figure
Most of the published research work related to the fatigue life of porous, high-pressure, die-cast structures is limited to a consideration of individual isolated pores. The focus of this article is on calculating the fatigue life of high-pressure, die-cast, AlSi9Cu3 parts with many clustered macro pores. The core of the presented methodology is a geometric parameterisation of the pores using a vector-segmentation technique. The input for the vector segmentation is a μ-CT scan of the porous material. After the pores are localised, they are parameterised as 3D ellipsoids with the corresponding orientations in the Euclidian space. The extracted ellipsoids together with the outer contour are then used to build a finite-element mesh of the porous structure. The stress–strain distribution is calculated using Abaqus and the fatigue life is predicted using SIMULIA fe-safe. The numerical results are compared to the experimentally determined fatigue lives to prove the applicability of the proposed approach. The outcome of this research is a usable tool for estimating the limiting quantity of a structure’s porosity that still allows for the functional performance and required durability of a product.
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