No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

For simple fluids, or Newtonian fluids, the study of the Navier-Stokes equations in the high Reynolds number limit brings about two fundamental research subjects, the Euler equations and the Prandtl's system. The consideration of infinite Reynolds number reduces the Navier-Stokes equations to the Euler equations, both of which are dealing with the entire flow region. Prandtl's system consists of the governing equations of the boundary layer, a thin layer formed at the wall boundary where viscosity cannot be neglected. In this dissertation, we investigate the upper convected Maxwell(UCM) model for complex fluids, or non-Newtonian fluids, in the high Weissenberg number limit. This is analogous to the Newtonian fluids in the high Reynolds number limit. We present two well-posedness results. The first result is on an initial-boundary value problem for incompressible hypoelastic materials which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume the stress tensor is rank-one and develop energy estimates to show the problem is locally well-posed. Then we show the more general case can be handled in the same spirit. This problem is closely related to the incompressible ideal magneto-hydrodynamics (MHD) system. The second result addresses the formulation of a time-dependent elastic boundary layer through scaling analysis. We show the well-posedness of this boundary layer by transforming to Lagrangian coordinates. In contrast to the possible ill-posedness of Prandtl's system in Newtonian fluids, we prove that in non-Newtonian fluids the stress boundary layer problem is well-posed. / Ph. D.

Ionomeric polymer transducers exhibit electromechanical coupling capabilities. The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers (IPTs). The research presented in this dissertation focuses on modeling the cation transport and cation steady state distribution due to the actuation of an IPT. Ion transport in the IPT depends on the morphology of the hydrated Nafion membrane and the morphology of the metal electrodes. Recent experimental findings show that adding conducting powders at the polymer-conductor interface increases the displacement output. However, it is difficult for a traditional continuum model based on transport theory to include morphology in the model. In this dissertation, a two-dimensional Monte Carlo simulation of ion hopping has been developed to describe ion transport in materials that have fixed and mobile charge similar to the structure of the ionic polymer transducer. In the simulation, cations can hop around in a square lattice. A step voltage is applied between the electrodes of the IPT, causing the thermally-activated hopping between multiwell energy structures. By sampling the ion transition time interval as a random variable, the system evolution is obtained. Conducting powder spheres have been incorporated into the Monte Carlo simulation. Simulation results demonstrate that conducting powders increase the ion conductivity. Successful implementation of parallel computation makes it possible for the simulation to include more powder spheres to find out the saturation percentage of conducting powders for the ion conductivity. To compare simulation results with experimental data, a multiscale model has been developed to increase the scale of Monte Carlo simulation. Both transient responses and steady state responses show good agreement with experimental measurements. / Ph. D.

The emerging field of nanomechanics is providing a new focus in the study of the mechanics of materials, particularly in simulating fundamental atomic mechanisms involved in the initiation and evolution of damage. Simulating fundamental material processes using first principles in physics strongly motivates the formulation of computational multiscale methods to link macroscopic failure to the underlying atomic processes from which all material behavior originates. A combined concurrent and sequential multiscale methodology is developed to analyze fracture mechanisms across length scales. Unique characterizations of grain boundary fracture mechanisms in an aluminum material system are performed at the atomic level using molecular dynamics simulation and are mapped into cohesive zone models for continuum modeling within a finite element framework. Fracture along grain boundaries typically exhibit a dependence of crack tip processes (i.e. void nucleation in brittle cleavage or dislocation emission in ductile blunting) on the direction of propagation due to slip plane orientation in adjacent grains. A new method of concurrently coupling molecular dynamics and finite element analysis frameworks is formulated to minimize the overall computational requirements in simulating atomistically large material regions. A sequential multiscale approach is advanced to model microscale polycrystal domains in which atomistically-based cohesive zone parameters are incorporated into special directional decohesion finite elements that automatically apply appropriate ductile or brittle cohesive properties depending on the direction of crack propagation. The developed multiscale analysis methodology is illustrated through a parametric study of grain boundary fracture in three-dimensional aluminum microstructures. / Ph. D.