Continuum limits of bistable spring models of carbon nanotube arrays accounting for material damage

TL;DR

This paper develops a mathematical model using chains of bistable springs to analyze the plastic behavior and damage accumulation in carbon nanotube arrays, demonstrating convergence to a continuum limit through analytical and numerical methods.

Contribution

It introduces a novel continuum limit model for damaged carbon nanotube arrays based on Gamma-convergence analysis of bistable spring chains.

Findings

Analytical stress-strain patterns for fatigue damage.

Numerical confirmation of the continuum limit convergence.

Insights into preconditioning effects due to loading history.

Abstract

Using chains of bistable springs, a model is derived to investigate the plastic behavior of carbon nanotube arrays with damage. We study the preconditioning effect due to the loading history by computing analytically the stress-strain pattern corresponding to a fatigue-type damage of the structure. We identify the convergence of the discrete response to the limiting case of infinitely many springs, both analytically in the framework of Gamma-convergence, as well as numerically.