Nature of short high amplitude pulses in a periodic dissipative laminate metamaterial

TL;DR

This paper investigates how high amplitude stress pulses propagate in periodic dissipative laminates made of aluminum and tungsten, revealing their solitary wave-like behavior and proposing a theoretical model based on a Korteweg de Vries type equation.

Contribution

It introduces a novel theoretical framework for describing high amplitude dissipative pulses in laminates, incorporating nonlinear constitutive behavior and mesostructural effects.

Findings

Localized waves resemble solitary waves despite dissipation

Pulse speed has a linear relationship with amplitude

The shape and scale of pulses depend on the laminate's mesostructure

Abstract

We study the evolution of high amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum and Tungsten laminate was taken as an example due to the large difference in acoustic impedances of aluminum and tungsten, the significant nonlinearity of aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls internal time scale, impacted by the plates with different thicknesses, determining the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high amplitude dissipative propagating waves, the oscillatory shock like profile, the train of localized pulses or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: the similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates, their characteristic length scale is determined by the mesostructural scale and the stress amplitude, and they mostly recover their shapes after collision with phase shift and a linear relationship exists between their speed and amplitude. A theoretical description approximating the shape, length scale and speed of these high amplitude dissipative pulses was proposed based on the Korteweg de Vries type equation with a dispersive term dictated by the mesostructure. The nonlinear term is derived from nonlinear constitutive equations of Aluminum and Tungsten, which were extracted from their Hugoniot curves.