Modeling the mechanics of soft particles using nonlinear membrane theory

Recently there has been great research interest in small soft particles because of their significance in both biology and industry. The term 'particle' here is defined as a deformable object with size in the range of nano- to micrometers. Many experimental efforts have been spent on investigating the behavior of these particles and theoretical models have been proposed to describe the mechanics of these particles under different loading conditions. Due to the complex nature of these particles, these mechanics models are all accompanied by various assumptions, one of the common simplifications being the neglect of large deformation. The objective of this study was to use nonlinear continuum based membrane theory in describing the mechanical behavior of soft particles under several loading conditions relevant to practice. In all cases studied, the particle was assumed to be spherical in the unstressed state and filled with incompressible fluid. The surface of the particle was considered to be homogenous, isotropic, of hyperelastic material and can sustain large nonlinear deformation. The particle was subjected to four different loading conditions: (1) symmetric poking by two identical conical indenters; (2) asymmetric poking by a conical indenter and a flat indenter; (3) micropipette aspiration; and (4) electrostatic attraction to a charged substrate. Under each condition, the deformation of the particle, its stress state and formation of contact were determined. Possible coupling between external loading and deformation was addressed. The theoretical results were compared with experimental results involving the mechanical response of soft particles such as cells. The model developed in this dissertation is capable of characterizing certain phenomena observed in experiments. The proposed model investigates the large deformation in soft particles from a continuum perspective. The model will be useful in understanding the mechanical properties of particles such as cells, vesicle and microcapsules that have an immense importance in life and industrial applications.