Transport codes are beginning to be parallelized in order to allow more complex add-ons, such as geochemical packages, to utilize finer, more accurate grids, and to reduce solution times making stochastic and Monte Carlo simulations more feasible. Most codes parallelized via MPI (message passing interface) offer good results, but require the development of a new parallel code. OpenMP, the shared-memory standard, offers incremental parallelization, allowing sequential codes to remain relatively intact with minimal changes or additions. OpenMP allows speedup to be seen on personal computers with dual processors or greater, unlike some other parallelization approaches that require a supercomputer. An operator-split strategy creates an environment for easy parallelization by decoupling the transport and reactions of species. The transport, when decoupled from the reactions, is dependent on surrounding nodes and not on species. Therefore, each species transport can be solved on a different processor. The reactions, when decoupled from the transport, are dependant on the other species concentrations and not on the surrounding nodes, allowing the concentrations for all species to be solve for at a given node as if in a batch reactor. This allows a parallelization of the nodes. Two codes are parallelized in this work. The first is a 100-species 1D theoretical problem. The second is RT3D, a modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater systems written and developed by Dr. T. Prabhakar Clement. RT3D is a sub-component of a parent code, MT3DMS, which utilizes RT3D to solve reaction terms. A speedup factor of 3.91 is seen on four processors, accomplishing a processor efficiency of approximately 98% while spent in RT3D itself.

The aim of this work is to develop and validate a continuum model for the simulation of the thermomechanical response of a shape memory polymer (SMP). Rather than integral type viscoelastic model, the approach here is based on the idea of two inter-penetrating networks, one which is permanent and the other which is transient together with rate equations for the time evolution of the transient network. We find that the activation stress for network breakage and formation of the material controls the gross features of the response of the model, and exhibits a "thermal Bauschinger effect". The model developed here is similar to a thermoviscoelastic model, and is developed with an eye towards ease of numerical solutions to boundary value problems. The primary hypothesis of this model is that the hysteresis of temperature dependent activation-stress plays a lead role in controlling its main response features. Validation of this hypothesis is carried out for the uniaxial response from the experimental data available in the literature for two different SMP samples: shape memory polyurethane and Veriflex, to show the control of the evolution of the temperature sensitive activation stress on the response. We extend the validated 1D model to a three dimensional small strain continuum SMP model and carry out a systematic parameter optimization method for the identification of the activation stress coefficients, with different weights given to different features of the response to match the parameters with experimental data. A comprehensive parametric study is carried out, that varies each of the model material and loading parameters, and observes their effect on design-relevant response characteristics of the model undergoing a thermomechanical cycle. We develop "response charts" for the response characteristics: shape fixity, shape recovery and maximum stress rise during cooling, to give the designer an idea of how the simultaneous variation of two of the most influential material parameters changes a specific response parameter. To exemplify the efficacy of the model in practical applications, a thermoviscoelastic extension of a beam theory model will be developed. This SMP beam theory will account for activation stress governed inelastic response of a SMP beam. An example of a three point bend test is simulated using the beam theory model. The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector. This algorithm is validated by using a three-point bending experiment for three different material cases: elastic, plastic and thermoplastic response. Time step convergence and mesh density convergence studies are carried out for the thermoviscoelastic FEM model. We implement and study this model for a SMP beam undergoing three-point bending strain recovery, stress recovery and cyclic thermomechanical loading. Finally we develop a thermodynamically consistent finite continuum model to simulate the thermomechanical response of SMPs. The SMP is modeled as an isotropic viscoplastic material where thermal changes govern the evolution of the activation stress of the material. The response of the SMP in a thermomechanical cycle is modeled as a combination of a rubbery and a glassy element in series. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. We use the technique of upper triangular decomposition for developing the constitutive equations of the finite strain SMP model. The resulting model is implemented in an ODE solver in MATLAB, and solved for a simple shear problem. We study the response of the SMP model for shear deformation as well as cyclic shear deformation at different initial temperatures. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.