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Modeling and Simulation of Inelastic Effects in Composite Cables

Davide Manfredo, Vanessa Dörlich, Joachim Linn, Martin Arnold

Abstract

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.

Modeling and Simulation of Inelastic Effects in Composite Cables

Abstract

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.
Paper Structure (6 sections, 7 equations, 4 figures)

This paper contains 6 sections, 7 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Hysteresis operators
  3. Relay operator
  4. Preisach operator
  5. Problem formulation
  6. First results and conclusion

Figures (4)

  • Figure 1: Left: cross sections of different electric cables. Centre: pure bending test rig. Right: bending moment vs. bending curvature diagram measured in a pure bending experiment.
  • Figure 2: Left: input function $v(t)=\sin(t)$, with $t\in[0,10]$. Centre diagram of the relay operator with $a_1=-0.3$ and $a_2=0.2$. Right: output function $w(t)=\mathcal{R}_{a_1,a_2}[v](t)$, with initial value $\xi=+1$.
  • Figure 3: Top left: input given as curvature vs. time. Top right domain (black rectangle) included in the Preisach plane with two examples of memory curve. Bottom: domain included in the Preisach plane with the triangulation and a memory curve for a given time $t_j$.
  • Figure 4: Left: kernel function obtained by the minimisation of $g$. Right: estimated plot of bending moment vs. curvature obtained by means of the hysteresis operator.