Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials

TL;DR

This paper develops a phase-space analysis of elastic vector solitons in flexible mechanical metamaterials, providing a revised continuum model that accurately predicts soliton properties with improved agreement to numerical simulations.

Contribution

It introduces a new continuum model derived from a discrete system, enabling phase-plane analysis of solitons in mechanical metamaterials, with enhanced accuracy over previous models.

Findings

Soliton amplitudes and velocities closely match numerical simulations.

The model improves prediction accuracy by exactly 1/9 over previous benchmarks.

The analysis confirms the existence of sech^2 soliton solutions in the system.

Abstract

The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane - a second-order nonlinear ODE related to the Klein-Gordon equation with quadratic nonlinearity. These admit the well-known $\mathrm{sech}^2$ solutions, which we employ as an ans\"atz following [Deng et.al., PRL, 2017]. The resulting analysis yields soliton amplitudes and velocities that agree closely with numerical simulations, achieving an improvement of exactly 1/9 relative to the benchmark reported by the Harvard group.