Multiscale constitutive modeling of polymer materials

Materials are inherently multi-scale in nature consisting of distinct characteristics at various length scales from atoms to bulk material. There are no widely accepted predictive multi-scale modeling techniques that span from atomic level to bulk relating the effects of the structure at the nanometer (10-9 meter) on macro-scale properties. Traditional engineering deals with treating matter as continuous with no internal structure. In contrast to engineers, physicists have dealt with matter in its discrete structure at small length scales to understand fundamental behavior of materials. Multiscale modeling is of great scientific and technical importance as it can aid in designing novel materials that will enable us to tailor properties specific to an application like multi-functional materials. Polymer nanocomposite materials have the potential to provide significant increases in mechanical properties relative to current polymers used for structural applications. The nanoscale reinforcements have the potential to increase the effective interface between the reinforcement and the matrix by orders of magnitude for a given reinforcement volume fraction as relative to traditional micro- or macro-scale reinforcements. To facilitate the development of polymer nanocomposite materials, constitutive relationships must be established that predict the bulk mechanical properties of the materials as a function of the molecular structure. A computational hierarchical multiscale modeling technique is developed to study the bulk-level constitutive behavior of polymeric materials as a function of its molecular chemistry. Various parameters and modeling techniques from computational chemistry to continuum mechanics are utilized for the current modeling method. The cause and effect relationship of the parameters are studied to establish an efficient modeling framework. The proposed methodology is applied to three different polymers and validated using experimental data available in literature.

Identifying indicators of sustainable development using the global sustainability quadrant approach

Advances in information technology and global data availability have opened the door for assessments of sustainable development at a truly macro scale. It is now fairly easy to conduct a study of sustainability using the entire planet as the unit of analysis; this is precisely what this work set out to accomplish. The study began by examining some of the best known composite indicator frameworks developed to measure sustainability at the country level today. Most of these were found to value human development factors and a clean local environment, but to gravely overlook consumption of (remote) resources in relation to nature’s capacity to renew them, a basic requirement for a sustainable state. Thus, a new measuring standard is proposed, based on the Global Sustainability Quadrant approach. In a two‐dimensional plot of nations’ Human Development Index (HDI) vs. their Ecological Footprint (EF) per capita, the Sustainability Quadrant is defined by the area where both dimensions satisfy the minimum conditions of sustainable development: an HDI score above 0.8 (considered ‘high’ human development), and an EF below the fair Earth‐share of 2.063 global hectares per person. After developing methods to identify those countries that are closest to the Quadrant in the present‐day and, most importantly, those that are moving towards it over time, the study tackled the question: what indicators of performance set these countries apart? To answer this, an analysis of raw data, covering a wide array of environmental, social, economic, and governance performance metrics, was undertaken. The analysis used country rank lists for each individual metric and compared them, using the Pearson Product Moment Correlation function, to the rank lists generated by the proximity/movement relative to the Quadrant measuring methods. The analysis yielded a list of metrics which are, with a high degree of statistical significance, associated with proximity to – and movement towards – the Quadrant; most notably: Favorable for sustainable development: use of contraception, high life expectancy, high literacy rate, and urbanization. Unfavorable for sustainable development: high GDP per capita, high language diversity, high energy consumption, and high meat consumption. A momentary gain, but a burden in the long‐run: high carbon footprint and debt. These results could serve as a solid stepping stone for the development of more reliable composite index frameworks for assessing countries’ sustainability.

MULTISCALE EXAMINATION AND MODELING OF ELECTRON TRANSPORT IN NANOSCALE MATERIALS AND DEVICES

For half a century the integrated circuits (ICs) that make up the heart of electronic devices have been steadily improving by shrinking at an exponential rate. However, as the current crop of ICs get smaller and the insulating layers involved become thinner, electrons leak through due to quantum mechanical tunneling. This is one of several issues which will bring an end to this incredible streak of exponential improvement of this type of transistor device, after which future improvements will have to come from employing fundamentally different transistor architecture rather than fine tuning and miniaturizing the metal-oxide-semiconductor field effect transistors (MOSFETs) in use today. Several new transistor designs, some designed and built here at Michigan Tech, involve electrons tunneling their way through arrays of nanoparticles. We use a multi-scale approach to model these devices and study their behavior. For investigating the tunneling characteristics of the individual junctions, we use a first-principles approach to model conduction between sub-nanometer gold particles. To estimate the change in energy due to the movement of individual electrons, we use the finite element method to calculate electrostatic capacitances. The kinetic Monte Carlo method allows us to use our knowledge of these details to simulate the dynamics of an entire device— sometimes consisting of hundreds of individual particles—and watch as a device ‘turns on’ and starts conducting an electric current. Scanning tunneling microscopy (STM) and the closely related scanning tunneling spectroscopy (STS) are a family of powerful experimental techniques that allow for the probing and imaging of surfaces and molecules at atomic resolution. However, interpretation of the results often requires comparison with theoretical and computational models. We have developed a new method for calculating STM topographs and STS spectra. This method combines an established method for approximating the geometric variation of the electronic density of states, with a modern method for calculating spin-dependent tunneling currents, offering a unique balance between accuracy and accessibility.

USING INDICATORS OF BIOTIC INTEGRITY FOR ASSESSMENT OF STREAM CONDITION

Multiple indices of biotic integrity and biological condition gradient models have been developed and validated to assess ecological integrity in the Laurentian Great Lakes Region. With multiple groups such as Tribal, Federal, and State agencies as well as scientists and local watershed management or river-focused volunteer groups collecting data for bioassessment it is important that we determine the comparability of data and the effectiveness of indices applied to these data for assessment of natural systems. We evaluated the applicability of macroinvertebrate and fish community indices for assessing site integrity. Site quality (i.e., habitat condition) could be classified differently depending on which index was applied. This highlights the need to better understand the metrics driving index variation as well as reference conditions for effective communication and use of indices of biotic integrity in the Upper Midwest. We found the macroinvertebrate benthic community index for the Northern Lakes and Forests Ecoregion and a coldwater fish index of biotic integrity for the Upper Midwest were most appropriate for use in the Big Manistee River watershed based on replicate sampling, ability to track trends over time and overall performance. We evaluated three sites where improper road stream crossings (culverts) were improved by replacing them with modern full-span structures using the most appropriate fish and macroinvertebrate IBIs. We used a before-after-control-impact paired series analytical design and found mixed results, with evidence of improvement in biotic integrity based on macroinvertebrate indices at some of the sites while most sites indicated no response in index score. Culvert replacements are often developed based on the potential, or the perception, that they will restore ecological integrity. As restoration practitioners, researchers and managers, we need to be transparent in our goals and objectives and monitor for those results specifically. The results of this research serve as an important model for the broader field of ecosystem restoration and support the argument that while biotic communities can respond to actions undertaken with the goal of overall restoration, practitioners should be realistic in their expectations and claims of predicted benefit, and then effectively evaluate the true impacts of the restoration activities.

MULTISCALE MODELING OF LIQUID CRYSTALLINE/NANOTUBE COMPOSITES

The objective of this research is to synthesize structural composites designed with particular areas defined with custom modulus, strength and toughness values in order to improve the overall mechanical behavior of the composite. Such composites are defined and referred to as 3D-designer composites. These composites will be formed from liquid crystalline polymers and carbon nanotubes. The fabrication process is a variation of rapid prototyping process, which is a layered, additive-manufacturing approach. Composites formed using this process can be custom designed by apt modeling methods for superior performance in advanced applications. The focus of this research is on enhancement of Young's modulus in order to make the final composite stiffer. Strength and toughness of the final composite with respect to various applications is also discussed. We have taken into consideration the mechanical properties of final composite at different fiber volume content as well as at different orientations and lengths of the fibers. The orientation of the LC monomers is supposed to be carried out using electric or magnetic fields. A computer program is modeled incorporating the Mori-Tanaka modeling scheme to generate the stiffness matrix of the final composite. The final properties are then deduced from the stiffness matrix using composite micromechanics. Eshelby's tensor, required to calculate the stiffness tensor using Mori-Tanaka method, is calculated using a numerical scheme that determines the components of the Eshelby's tensor (Gavazzi and Lagoudas 1990). The numerical integration is solved using Gaussian Quadrature scheme and is worked out using MATLAB as well. . MATLAB provides a good deal of commands and algorithms that can be used efficiently to elaborate the continuum of the formula to its extents. Graphs are plotted using different combinations of results and parameters involved in finding these results