Prestrain-induced contraction in 1D random elastic chains

TL;DR

This paper investigates how prestrain causes contraction in one-dimensional elastic chains, combining simulations and analysis to show that such chains always shrink regardless of topology or connectivity.

Contribution

The study introduces a minimal 1D model for prestrained elastic networks and demonstrates the universal contraction behavior through analytical and numerical methods.

Findings

Chains always shrink under prestrain.

Contraction magnitude depends on prestrain variance.

Results are robust across different topologies.

Abstract

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider a minimal model in one dimension. We do this by considering a chain (1D network) of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain and consider more complex connectivity and show that our results are relatively robust to these changes.