PSI - Issue 37

Tomasz Rogala et al. / Procedia Structural Integrity 37 (2022) 187–194 / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. A 3D objects representing subsequently crack, delamination and more degradated object with crack dominated class

Due to the fact that this type of damage has the form of longitudinal and narrow elements, it was decided that this class would be represented by an ellipsoid that meets the following conditions: ● its centre coincides with the centre of analysed object, ● its orientation in the space will be determined by the direction of principal axes which correspond to the directions of the principal axes of an analysed object, ● its size represented by the values of semi axes allows to obtain the same moments of inertia in comparison to an object. The above mentioned conditions allow to obtain an reference (equivalent in the sense of above mentioned conditions) object which is an instance of the ellipsoid class. The reference object is defined for every damage object and is further used to describe its similarity to the reference object in two dimensional space. In order to obtain transformation of a three dimensional damaged object into the two dimensional space the following operations are performed: ● a boolean product operation between the equivalent reference object and damage object is performed, ● the external surface of the boolean product operation is discretized by meshing its surface using triangular mesh ● then for each node position of the meshed surface the following spherical transformation is performed ⋁ [ , , ] => [ ( ) ; ( √ 2 + 2 ) ], (1) where the obtained values stand for position of node in the two dimensional space. In figure 3. some initial stages of changing a three dimensional object into two dimensional representation are presented. For the sake of simplicity, the operations are shown on the example of an artificial object represented by cuboid. It should be emphasized that the obtained equivalent object in the form of an ellipsoid is the reference object. As a result of applying a boolean operation between the original object and the equivalent ellipsoid, a new object is created. This new object is transformed into a two-dimensional form (Fig. 3b). The obtained object can be interpreted as an object which shows how similar these objects are (reference object and analyzed object). The two-dimensional measures obtained in the further process are mostly a description of the morphology of the shape of the obtained object. The transformation presented here was partly inspired by the publication on fractal dimensions in Zhoe at all., (2018). Figure 3c shows the created mesh of triangular elements on the surface of the formed object using tool available by (Fang and Boas, 2009). As a result of applying the transformation, this object is transformed into a two dimensional image, e.g. Fig 3d. A result of transforming a three-dimensional element into a two-dimensional plane, the geometrical property of the longitudinal elements being transformed into a flat longitudinal figure is preserved. Also, an ellipsoid-like object will have the form of an ellipse in two-dimensional space. On the other hand, objects significantly different in shape from the reference ellipsoid will have the shape of a figure, in the two-dimensional space, with the contours which will not