The present work aims at describing hysteresis behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. Pure bending experiments conducted in previous work show that 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. Here, we utilise data collected from pure bending experiments for a first approach. We introduce a mathematical formulation of the problem, and starting from the curvature of the cable specimen, we recursively define the Preisach plane for this specific case. Therefore, we derive a suitable kernel function in a way that the integration of such function over the Preisach plane results in the bending moment of the specimen.

翻译：本研究旨在利用Preisach算子描述电缆在循环弯曲实验中产生的迟滞行为。前人工作中进行的纯弯曲实验表明，电缆等细长结构呈现非弹性特性，并产生开放的迟滞回线，首次加载循环与后续循环之间存在显著差异。Preisach算子在描述迟滞行为的输入输出关系中扮演重要角色，可表示为继电算子的叠加。本文基于纯弯曲实验收集的数据进行初步探究。我们引入问题的数学表述，从电缆试件的曲率出发，针对这一特定情况递归地定义Preisach平面。进而，我们推导出合适的核函数，使该函数在Preisach平面上的积分结果对应于试件的弯矩。