Linking and Unifying Atomistic and Continuum Mechanics Formulation        

        Development of multiscale simulation methodologies was identified to be a major focus of Simulation-Based Engineering & Science research in the 2006 NSF Blue Ribbon Panel Report and again in the 2009 WTEC Panel Report on Simulation-Based Engineering & Science   Despite of decades of intense effort from researchers in many disciplines, however, there has been no successfully-developed general multiscale simulation methodology to date. A key challenge in the development of multiscale methods is to interface atomistic models with continuum mechanics, since across this atomistic-continuum interface there is a change in system description and governing equations, and consequently phonon scattering/wave reflections at the artificial interface. This in turn fundamentally alters the dynamic material behavior in simulation, rendering most of the multiscale methods powerless in simulations of dynamic phenomena.

          This research aims to meet this challenge by answering two fundamental questions: (1) can we unify atomistic and continuum formulation so as to develop a concurrent multiscale methodology within one single theoretical framework, rather than combining two different methods in one model? (2) can we allow waves, heat and defects  propagate from the atomistic region into the continuum region and vice versa, rather than absorbing them at the interface?  To answer these two questions, we are developing a new formalism that analytically links atomistic variables to continuous local density functions and that will lead to a field representation of the governing laws of atomistic systems, with which a material is described as a continuous collection of material points but embedded within each material point is a group of atoms. We anticipate that this research will lead to the formulation of a new theory of continuum mechanics that is equivalent to a fully atomistic model at fine scale and can be reduced to the classical continuum mechanics at the macroscopic scale.


Prediction of Thermal Transport Properties of Materials with Microstructural Complexity

        The ability to design and control the microstructure of materials promises revolutionary advances in new materials development. In addition to the processing technology for precise control of materials microstructure at the nanometer to micron scales, the most formidable challenge in developing this ability is to predict the material properties from its chemical composition and multiscale microstructural features. No simulation tool currently exists for such prediction. This research aims to meet this challenge by (a) establishing a concurrently coupled atomistic-continuum methodology that can be used to design and optimize materials with microstructural complexity, and (b) demonstrating the methodology through predicting the mechanical and thermal transport properties of thermoelectric materials and comparing the predictions with experimental measurements.         

         We choose thermoelectric materials, i.e., materials that convert heat into electricity and that may play an important role in a global sustainable energy solution, because (1) to develop high-efficiency thermoelectric materials one needs to minimize the thermal conductivity while maximizing the electrical conductivity; however, there are currently no theoretical tools to predict thermal conductivity of complex thermoelectric materials; (2) many thermoelectric materials are well tested; the rich pool of information about their molecular and micro-structure as well as their mechanical and thermal transport properties has set the stage not only for predictive simulation tools to be validated but also for computational research to provide additional insights and to obtain missing information that cannot be accessed by current experimental techniques. 


Collaborative Research: Novel Atomistic-Continuum Simulation of Sequential Grain Boundary-Dislocation Slip Transfer Reactions

          The objective of this collaborative research project is to advance the CAC simulation method to explore slip transfer at grain boundaries. Lack of such a method is a current obstacle to progress towards developing constitutive relations that reflect the structure and behavior of grain boundaries, for example in polycrystal plasticity. The problem is complicated by the need to account for long range interactions of dislocation fields while also considering the atomic-level structural detail of the interface.

         This research will explore processes of sequential dislocation reactions with bicrystal interfaces by maintaining full atomistic resolution of the interface reactions and successively coarse graining the field description away from the interfaces at distances that are normally inaccessible to fully resolved molecular dynamics. Such a capability will enable parametric studies of dislocation-grain boundary slip transfer reactions over the full range of grain boundary degrees of freedom, including tilt and twist boundaries, as well as asymmetric boundaries that often have faceted structure and can give rise to profuse dislocation nucleation. Nanotwinned structures with a wide range of twin spacing will also be considered. This work will use state-of-the-art embedded atom method potentials which have proven quite accurate for fcc metals such as Cu in modeling various aspects of dislocation nucleation, formation of stacking faults, and dislocation interactions.


Towards Multiscale Mechanical Design of Hierarchical Cellular Materials

          Cellular materials are a specific class of highly porous materials characterized by the presence of a recognizable ‘cell’, or ‘cells’, that is an empty space possessing solid edges and faces (Colombo 2005).  Because of their porous structure, they display a unique combination of properties, such as low density, low thermal conductivity, low dielectric constant, high specific strength, high permeability, high thermal shock resistance, high wear resistance, and high resistance to chemical corrosion, making them indispensable in various advanced engineering applications. Novel application examples include low dielectric constant materials for next generation microelectronics, low thermal conductivity materials for thermal management under extreme environments, high porosity materials for electrodes in fuel cells technology, and highly porous scaffolds for tissue engineering. In all of these emerging technologies porous material must be involved, and the porosity is a key to their performance. However, at present the porosity and hence their functionality is limited by the mechanical properties. The fast degradation of the strength, stiffness and toughness as a result of increasing porosity is one of the most critical issues in all applications of cellular/porous materials. Consequently a key challenge in materials engineering is to design cellular materials that simultaneously have high strength, toughness, stiffness, as well as high porosity.

        Wood is an example of an extraordinary cellular material that is highly porous yet lightweight, strong, stiff, hard and tough, a combination rarely seen in man-made materials. Wood has strength per unit weight comparable with that of the strongest steel. Wood has fracture toughness several magnitudes greater than that of most of man-made porous/cellular materials. Wood is also well known for its hardness, for its matchless durability and great tolerance to damage. The surprise, however, is that there is nothing very special about its building blocks, rather there has been a strong belief that wood owes its extraordinary mechanical properties to its hierarchical architecture. 

       Understanding the effect of hierarchical structure on wood’s extraordinary mechanical properties offers an opportunity to leapfrog current cellular materials technology. Our long term objective is to hierarchically design cellular materials that have high porosity as well as desired mechanical properties. The objective of this project is to use computational and experimental analyses to create a fundamental understanding of how the multiscale structural organization of wood determines its mechanical properties and to discover design principles that may apply generally to multiscale hierarchical design of synthetic cellular materials.


Reproducing the Extraordinary Mechanical Properties of Biominerals through Multiscale Simulation

        The term biomineral refers to mineralized biological materials. Calcium carbonate (CaCO3) minerals are the most abundant biominerals both in terms of the quantities produced and their widespread distribution. The most-studied calcium carbonate biomineral is nacre (the inside portion of shells). Nacre is a 95-99% crystalline calcium carbonate by volume or 99-99.5% by mass. It is an exceptionally remarkable mineral material in that it has a rare combination of high strength, high toughness, high stiffness and high hardness. Even more remarkable is that, with the addition of less than 1% organic materials, it is 20 time stronger and 3000 times more fracture resistant (in terms of work of fracture) than pure calcium carbonate crystalline materials.

        These extraordinary mechanical properties have stimulated many fields of researchers. Despite considerable efforts, however, our understanding of the mechanisms that operate in nacre making it a simultaneously tough, strong and hard composite is still limited. Although improvements were achieved in the mechanical properties of mimics of nacre, none has been as extraordinary as when nacre is compared to monolithic CaCO3. To date, no one has ever produced a CaCO3 composite that can approach the mechanical properties of nacre or a ceramic-polymer composite that is 20 times stronger and 3000 times tougher than the ceramic material with less than 1% addition of polymeric materials by synthesis or by computer.

       This project aims to understand the exceptional mechanical properties of biominerals through molecular and multiscale simulations. Nacre is chosen to be reproduced in simulation because: (1) it is the most-studied biomineral by experimental researchers in many fields and yet limited success in its biomimetic products has been achieved; (2) many of the macromolecules in other biominerals are unknown or have not been sequenced, but they are relatively well investigated in nacre; and (3) the rich pool of information about its architecture and composition has set the stage for computational research to provide additional insights and to obtain missing information, usually fine scale information or multiscale interaction, that cannot be accessed by present experimental techniques

A photo of nacre