Mechanical response of soft matter systems: biological tissues and wrinkled structures

Abstract

In recent years, there has been a significant growing interest in developing an understanding of soft materials due to their rich properties and wide applications. In this thesis, I present a study on the mechanical response properties of two types of soft materials: biological tissues and wrinkled structures. Epithelial tissues consist of thousands of cells moving in groups, which is commonly simulated with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically study the full dynamic range of shear and bulk rheology and measure the dynamical response modulus. We show that the linear viscoelastic responses of the vertex model could be mapped to standard spring-dashpot models. I further develop a normal mode formalism that can describe the linear viscoelastic properties of soft elastic systems with different microscopic dissipation mechanisms. We show that the motion along each normal mode behaves independently as a spring-dashpot model. The values of spring constants and dashpot viscosity can be naturally related to the corresponding eigenvalues and the projection of external driving without the need for any fitting parameter. Besides, we show that extending the vertex model to include different types of microscopic dissipation mechanisms has non-trivial effects on rheology, which are captured by the normal mode formalism. Finally, I present the linear response theory of wrinkled structures. While the formation and evolution of wrinkled structures are well understood, more is needed to know how they respond to external forces and achieve their functions in various applications. Thus, we study how wrinkled structures respond to infinitesimal surface forces. We find that the linear response diverges near the onset of the wrinkling instability, which can be understood in terms of the dominant characteristic Fourier mode of wrinkles. However, the coupling between different Fourier modes becomes significant away from the instability threshold, affecting the mechanical response of the structures.