MODELING COMPLEX SURFACE MECHANICAL BEHAVIOR OF SOFT SOLIDS

Abstract

This dissertation presents part of my recent effort to understand complex surface mechanical phenomena in soft materials using theoretical modeling and computational simulation. Most conventional engineering materials resist deformation by their bulk mechanical properties, such as elasticity, plasticity, and the like. For these materials, the mechanical role of the surface is negligible. However, when a material is soft enough, surface stress can compete with and even dominate over the bulk response. For soft solids, the pervasive influence of surface stress requires re-thinking a wide range of mechanical phenomena and properties. Many works on surface mechanical behavior of soft materials focus on constant surface stress or time-independent elastic bulk deformation, neglecting surface elasticity or time-dependent deformation mechanisms such as poroelasticity or viscoelasticity in the bulk. Only recently, researchers interested in surface stress have begun to study the effects of surface elasticity or bulk poroelasticity on surface mechanical phenomena. In the first part of the dissertation, we review a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We demonstrate that the large deformation theory can be reduced to the classical linear theory (Shuttleworth Equation). We then provide exact solutions for two problems: inflation of a cylindrical shell and bending of a plate with a finite thickness. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures. Next, we propose and implement a specific strain-dependent surface stress finite element to simulate a quasi-static retraction process of a rigid sphere in adhesive contact with a soft silicone gel. Our simulation is in good agreement with experimental force versus displacement data with no fitting parameters, whereas the experimental data cannot be explained either by the Johnson–Kendall–Roberts (JKR) theory or a recent indentation theory based on an isotropic surface stress that is independent of surface strain. Our results lend further support to the claim that significant strain-dependent surface stresses can occur in simple soft elastic gels. Finally, we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow field are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending – it is bounded and continuous. We also use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.