Modeling and Simulation of Inelastic Effects in Composite Cables

Core Concepts

Modeling hysteresis behavior in composite cables using Preisach operators.

Abstract

The content discusses the hysteresis behavior observed in composite cables during cyclic bending experiments. It introduces the concept of Preisach operators to describe the input-output relation in hysteresis behaviors. The article outlines the mathematical formulation used to model the observed behavior and emphasizes the importance of understanding the interaction effects within electric cables. The study aims to minimize an expression by defining suitable kernel functions and approximating bending moments based on experimental data.

Introduction to Electric Cables and Hysteresis Behavior

Complex nature of electric cables due to multi-material composition.
Observations of open hysteresis loops in cyclic bending experiments.

Hysteresis Operators: Relay Operator and Preisach Operator

Description and application of relay operator for threshold crossing.
Introduction to Preisach operator as a superposition of relay operators with a kernel function.

Problem Formulation for Modeling Inelastic Deformation Behavior

Utilizing data from pure bending cyclic experiments for modeling.
Defining Preisach plane sets, memory curves, and minimizing an expression.

Results and Conclusion on Modeling Approach

Approximation of kernel function through minimization process.
Comparison between experimental data and modeled output relation.

Stats

Pure bending experiments show open hysteresis loops with differences between load cycles [1, 2].
The relay operator is introduced for threshold crossing [3].
The Preisach operator is defined as a superposition of relay operators with a kernel function [4].

Quotes

Key Insights Distilled From

Modeling and Simulation of Inelastic Effects in Composite Cables

by Davi... at arxiv.org 03-22-2024

https://arxiv.org/pdf/2403.13837.pdf

Deeper Inquiries

How can the findings on hysteresis behavior in composite cables be applied to other materials or structures

The findings on hysteresis behavior in composite cables can be applied to other materials or structures by providing a framework for understanding and modeling complex deformation behaviors. The use of Preisach operators allows for the description of hysteresis phenomena without specific assumptions on material behavior, making it applicable to a wide range of materials beyond composite cables. By studying how different materials exhibit inelastic deformation under cyclic loading, researchers can apply similar mathematical formulations to model and predict the behavior of various structures subjected to repetitive stress.

What are potential limitations or criticisms of using Preisach operators to model hysteresis phenomena

Potential limitations or criticisms of using Preisach operators to model hysteresis phenomena include the complexity involved in determining suitable kernel functions and accurately representing the input-output relation. The piecewise constant assumption over triangles may oversimplify the actual behavior, leading to potential inaccuracies in modeling real-world systems. Additionally, interpreting and analyzing the results obtained from Preisach operators require expertise in mathematics and computational methods, which could pose challenges for practitioners not well-versed in these areas.

How might advancements in mathematical frameworks like Preisach operators impact other fields beyond engineering

Advancements in mathematical frameworks like Preisach operators have the potential to impact other fields beyond engineering by offering a versatile tool for modeling complex hysteretic behaviors. In fields such as economics, neuroscience, or material science where nonlinear dynamics play a crucial role, Preisach operators could provide insights into system responses that exhibit memory-dependent properties. By applying similar principles used in engineering contexts to these diverse fields, researchers can gain a deeper understanding of how systems with memory effects behave under varying conditions. This cross-disciplinary application of advanced mathematical frameworks opens up new avenues for research and innovation across multiple domains.