A nonlinear acoustomechanical field theory of polymeric gels

Abstract

A nonlinear acoustomechanical field theory is presented for polymeric gels undergoing large deformation coupled with diffusion mass transport of solvent molecules in and out of the gel. The theory is developed by combining the acoustic radiation stress theory with the nonlinear elasticity theory of polymeric gels. Explicit velocity and acoustic fields are determined by solving the elastodynamical equations of wave propagation in Eulerian coordinates, which are then employed to determine the distribution of acoustic radiation stresses inside the gel. The nonlinear elasticity of gels is modeled by adopting the Flory–Rehner free energy functions for network stretching and molecules-polymer mixing. For illustration, the developed theory is applied to a layer of polymeric gel immersed in external solvent subjected to two counterpropagating acoustic waves. The acoustically actuated large deformation of the gel is analyzed under three different constraint conditions. Unique acoustomechanical behaviors of polymeric gels are revealed, such as periodical response and nonlinear chaos. This work is expected to enable novel design of ultrasound-triggered sensors and actuators made of polymeric gels, and can also enlighten the application of ultrasonic waves in biomedical engineering.