Optimization of a lattice spring model with elastoplastic conducting springs: A case study

TL;DR

This paper applies sweeping process theory to optimize elastoplastic lattice spring models with conducting springs, balancing response force and resistance for designing multi-functional materials.

Contribution

It introduces a novel application of sweeping process theory to optimize elastoplastic conducting spring systems, offering an alternative to topological optimization.

Findings

The model effectively predicts the response force during stretching.

Optimization balances resistance and terminal response force.

Method provides a practical tool for designing multi-functional materials.

Abstract

We consider a simple lattice spring model in which every spring is elastoplastic and is capable to conduct current. The elasticity bounds of spring $i$ are taken as $[-c_i,c_i]$ and the resistance of spring $i$ is taken as $1/c_i$, which allows us to compute the resistance of the system. The model is further subjected to a gradual stretching and, due to plasticity, the response force increases until a certain terminal value. We demonstrate that the recently developed sweeping process theory can be used to optimize the interplay between the terminal response force and the resistance on a physical domain of parameters $c_i.$ The proposed methodology can be used by practitioners for the design of multi-functional materials as an alternative to topological optimization.