Evidence of emergent scaling in mechanical systems

Abstract

In previous work, electrical networks of randomly distributed resistors and capacitors driven with a periodic voltage have shown emergent scaling behaviour: a logarithmic scaling rule is found to dictate the conductance of the bulk network as a function of frequency. This feature has also been shown in other bi-materials and is thought to be independent of the materials involved and, hence, “universal” in nature. The present article examines the potential universality of these scaling laws by considering a mechanically loaded random network. In particular, the mechanical network under consideration is a statically loaded truss. The mechanical system shows an emergent region and percolation paths, much like its electrical counterpart, further suggesting that random, networked systems may have a universal character.

Acknowledgements

The first author is indebted to the Institute for Complex Systems and the Centre for Nonlinear Mechanics at the University of Bath for hosting him during his sabbatical stage; and also acknowledges the financial support from the University of Connecticut Research Foundation during his leave.