First Steps in Data Based Constitutive Modelling of Inelastic Effects in Composite Cables Using Preisach Hysteresis Operators

Abstract

The present contribution aims at describing hysteresis behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically and open hysteresis loops arise, with noticeable difference between the first load cycle and the following ones. The Preisach operator plays an important role in describing the input-output relation in hysteresis behaviours and it can be expressed as a superposition of relay operators. The definition of the Preisach plane occurs naturally from the definition of Preisach operator and hysteresis loops can be computed by integrating a suitable kernel function over a domain included in the Preisach plane. A mathematical formulation of the problem is introduced and a first attempt is made to mathematically determine the hysteresis behaviour that describes the relation between curvature and bending moment. Therefore, a suitable kernel function is identified in a way that its integration over the Preisach plane results in the bending moment of the specimen, and a comparison between different kernel functions is performed.

Neural networks for the approximation of Euler's elastica

“…In this work, we use neural networks to approximate the configurations of highly flexible slender structures modelled as beams. Such models are of great interest in industrial applications like cable car ropes, diverse types of wires or endoscopes [29][30][31][32]. Notwithstanding their ingenious and simple mathematical formulation, slender structure models can accurately reproduce complex mechanical behaviour and for this reason their numerical discretisation is often challenging.…”