Nonlinear response and axisymmetric wave propagation in functionally graded soft electro-active tubes

TL;DR

This paper investigates the nonlinear behavior and wave propagation in functionally graded soft electro-active tubes under various biasing fields, providing analytical models and numerical insights for improved design of SEA devices.

Contribution

It develops explicit nonlinear response models and analytical dispersion relations for wave propagation in graded SEA tubes under complex biasing conditions.

Findings

Material gradients significantly affect static nonlinear response.

Biasing fields influence axisymmetric wave speeds and behavior.

Analytical dispersion relations enable tunable waveguide design.

Abstract

Soft electro-active (SEA) materials can be designed and manufactured with gradients in their material properties, to modify and potentially improve their mechanical response in service. Here, we investigate the nonlinear response of, and axisymmetric wave propagation in a soft circular tube made of a functionally graded SEA material and subject to several biasing fields, including axial pre-stretch, internal/external pressure, and through-thickness electric voltage. We take the energy density function of the material to be of the Mooney-Rivlin ideal dielectric type, with material parameters changing linearly along the radial direction. We employ the general theory of nonlinear electro-elasticity to obtain explicitly the nonlinear response of the tube to the applied fields. To study wave propagation under inhomogeneous biasing fields, we formulate the incremental equations of motion within the state-space formalism. We adopt the approximate laminate technique to derive the analytical dispersion relations for the small-amplitude torsional and longitudinal waves superimposed on a finitely deformed state. Comprehensive numerical results then illustrate that the material gradients and biasing fields have significant influences on the static nonlinear response and on the axisymmetric wave propagation in the tube. This study lays the groundwork for designing SEA actuators with improved performance, for tailoring tunable SEA waveguides, and for characterizing non-destructively functionally graded tubular structures.