The enhanced hysteresis model is time efficient in transforming global analysis results into local stress and is capable of modelling the stress in nth order laid elements through n-gon described geometric shapes and a parameter scheme. It is thus applicable for shapes that can be described by a concave or convex 2D profile which enables detailed stress calculations of more complex shaped elements in subsea power cables, umbilicals and hybrids.


An effective and proficient stress model is needed to transform the global response of subsea power cables, umbilicals and hybrids into a local mechanical stress. Such a model must thus be able to process a large data volume within a short time frame and proficiently handle all element geometries that forms the bundled product. As a consequence Karlsen (2021) developed a novel and time efficient stress hysteresis model, for both non-helix and up to nth order helix laid circular elements, that combines calculated stress parameters with stress parameters from a local FEA tool. The model was named Adaptive Hysteresis Model (AHM) as it adapts to the stick-slip condition of element's lower order. The same author introduced another time effective approach in Karlsen (2022) for modelling the 1st order stress hysteresis, applicable for rectangular and squared shaped elements, based on stress parameters from a cross section analysis tool, element dimensions and material properties.

In subsea power cables however, such as the Oil Filled and Mass Impregnated (MI), profiled arc shaped strands are used to produce a conductor with a high fill factor and to give a smooth surface for the insulation, see Figure 1. Furthermore, during manufacturing of conductors used in XLPE and PEX power cables, DEHs (Direct Electrical Heating) and power umbilicals, the strands are bundled and most often compacted as they are pulled through a die. In this part of the process, the outermost positioned strand especially, which started as circular, tend to end up in a more trapezoid/pentagon shape. How much they are deformed is dependent on the required fill factor. In addition, most of the elements in such products are laid in helices, which will change elements’ geometry in a plane projection, see Figure 2. As the figure shows, a circular tube will not be completely circular in its projection. It will have a curved elliptic shape within its layer as it passes through the plane. As these latter described elements, and more, are considered to be neither circular or rectangular, the methods presented in Karlsen (2021) and (2022) are not directly applicable.

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