Pressure diffusion wave and shear wave in gels with tunable wave propagation properties

• Published in: Journal of the mechanics and physics of solids Vol. 134; p. 103736
• Main Authors: Wang, Bohan, Hu, Yuhang
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.01.2020; Elsevier BV
• Subjects: Anisotropy; Attenuation coefficients; Constitutive relationships; Crosslinking; Deformation; Diffusion rate; Diffusion waves; Elastic waves; Gels; Group velocity; Large deformation; Material properties; Organic chemistry; Phase velocity; Polymers; Propagation; S waves; Shear; Soft materials; Solvents; Wave propagation; Wave propagation; Anisotropy; Soft materials; Large deformation
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2019.103736

Gels are composed of cross-linked polymer network and solvent. Gels are both ubiquitous in nature and widely applied in engineering applications. In this work, we develop a physics-based dynamic theory to investigate the tunable wave propagation properties of gels. Gels are soft and can generate large deformation. The constitutive relation takes account the coupled large deformation and diffusion of gels. The dynamic governing equations take account the relative motions between the polymer network and solvent, which leads to a pressure diffusion wave similar to the “slow pressure wave” in the classical Biot’s poroelastodynamics. It is different from the pressure wave in pure solid or pure liquid. The phase velocity, group velocity and attenuation coefficient are analyzed at different frequencies and propagating directions for both pressure wave and shear wave. We show that the wave propagation properties of gels are not only related to the material properties including the crosslink density and the interaction property between solvent and polymer, but also can be tuned by different mechanical loading conditions and chemical stimuli. It is also predicted that the constrained swollen gel exhibits anisotropic wave propagation properties, which leads to the splitting of the pressure wave and shear wave propagating through it. The theory provides a general frame for fundamental understanding and quantitative characterization of the dynamic behaviors of gels.