Discrete particulate description of elastic structures undergoing geometrically nonlinear deformation and dynamic particle interaction

Abstract

The mechanical behaviour of deformable bodies in a particulate environment has been an area of increasing interest across a wide spectrum of systems and scale. A composite ensemble of deformable structures and discrete particles involves coupling of component responses, large displacements of structures, and multiple dynamic interactions that lead to inherent contact nonlinearity. To describe these structures and their interactions with particles, we apply a particle simulation approach based on the discrete element method (DEM). There exist alternative frameworks too such as continuum modelling with techniques like finite element method (FEM), or a combination of continuum and discrete modelling, or lumped modelling with mass-spring systems. Owing to the convenience and robustness provided by a single approach, this thesis aims to develop a single framework with the discrete modelling approach. The mechanical behaviour of particulate models of slender elastic continua is first validated with their analytical or FEM counterparts, and then particle-structure interactions are considered. We develop elastically deformable particulate models of straight beams and shallow arches. We evaluate the geometrically nonlinear response of particulate beams under a variety of static, dynamic, and impact loading scenarios. We also model particulate arches and assess their ability to exhibit two force-free equilibrium states, namely bistability. To illustrate the utility of these particulate representations, we first consider a case study of an undulating beam in a particle medium. The dynamic beam-particle interactions propel the beam within the medium, resembling the self-propulsion of reptiles in granular environments. In another case study, we take up a relatively sparse environment of mobile particles and oscillating cantilever beams. The interplay between particles and beams is shown to drive particles for capture. We also demonstrate particle-arch interactions in bistable mechanisms that result in particle gripping and trapping. We draw insights from factors that regulate the governing dynamics of such coupled phenomena. Next, we model particulate thin films that undergo deflections in linear and geometrically nonlinear regimes and describe both plate-like and membrane-like behaviours. A notable instance of this particulate perspective of thin films occurs in the context of microscopic biological material such as cells and their organelle. We present in this context a discrete particulate description for the nucleus of a biological cell. A three-dimensional model that incorporates the nuclear envelope and chromatin-containing nucleoplasm is developed and subjected to micropipette aspiration. Our work on particulate systems is implemented within Altair EDEM, a commercial DEM software. While most available DEM packages, including EDEM, provide a ready-to-use interface for the modelling and analysis of granular and bulk materials, they lack similar modules for particulate structures. The preprocessing stage thus involves substantive customization to build algorithms for particle generation, contact physics, external couplings, and parameter definition appropriate to our studies. By customizing this process, we utilize the graphical interface capabilities of EDEM to simulate, readjust, and visualize the analysis of structures under applied forces and particle interaction. Taken together, the studies in this thesis facilitate a comprehensive investigation of the particulate approach’s efficacy to model a variety of deformable structures, capture geometric nonlinearity in their response, and simulate the interaction dynamics of coupled particle-structure systems.