Acousto-thermo-mechanical deformation of hydrogels coupled with chemical diffusion.

We develop an acousto-thermo-mechanical theory for nonlinear (large) deformation of temperature-sensitive hydrogels subjected to temperature and ultrasonic inputs, with diffusion mass transport driven by osmotic pressure accounted for. On the basis of the strain energy due to network stretching, the mixing energy of polymers and small molecules, the Cauchy stress of the deformed hydrogel can be obtained. The acoustic radiation stress generated by the ultrasonic inputs is incorporated into the Cauchy stress to give the constitutive equations of the acousto-thermal-mechanical hydrogel. The mixing energy contains an interaction parameter as a function of temperature and polymer concentration so that hydrogel deformation is temperature dependent. By employing the incompressible condition of polymers and molecules, both the temperature and acoustic radiation stress contribute to osmotic pressure, inducing hydrogel swelling (or shrinking). Specifically, for a temperature-sensitive hydrogel layer immersed in solvent, its acoustic-triggered large deformation is comprehensively analysed under different boundary conditions (e.g. free swelling, uniaxial constraint and biaxial constraint).