CM2EM Research Projects
First-Principles Studies of Alloys
Metal alloys often form complex structures, including large unit cell crystals, quasicrystals and metallic glasses. Almost all metals in commercial use are alloys containing multiple chemical species, with compositions carefully tailored to achieve desired structures and properties. Predicting the structure and properties of any particular compound is a considerable challenge and is a necessary part of efforts to design new materials with improved performance. First-principles ab-initio calculations based on quantum mechanical electronic density functional theory provide insight into alloy structures at low temperatures as a result of their total energies, and insight into properties through their electronic and vibrational band structures. Applying principles of statistical mechanics allows us to extend this understanding to higher temperatures, and through molecular dynamics simulation we can reach the liquid state.
These calculational methods allow Professor Widom to explain mechanisms favoring the formation of bulk metallic glass for structural applications, and to tailor their mechanical properties to improve ductility, a project carried out in collaboration with experimentalists from the University of Virginia. In parallel with the metallic glass project, a database has been established (see http://alloy.phys.cmu.edu) containing crystal structures and their enthalpies of formation in hundreds of different binary, ternary and higher-order alloy systems. Similar methods have been used to predict the structure of quasicrystals and explain their thermodynamic stability.
Crystal Plasticity in Metallic Materials
The study of the solid mechanics of crystalline bodies of structural dimensions in the 1um - 10nm range requires the consideration of crystal lattice defects, the most common of which is the crystal dislocation. Examples of such structures are semiconductor thin films used in electronic devices (LEDs, transistors), and metallic interconnects in integrated circuitry and actuators in MEMS devices. It is well known that deformation microstructures in structural metals critically affect their response to loads - such microstructures are also the result of plasticity in the lengthscale range mentioned above. The goal of Professor Acharya's research in Field Dislocation Mechanics and its appropriate averaging is the understanding of single and polycrystalline plasticity from the nano to macro scales, with a view towards developing predictive theory and computational tools for deformation- induced microstructure evolution. Figure 2 shows the prediction of novel size effects and heterogeneity patterns in the micron-scale response of metallic materials that are in accord with recent experimental observations.
The Field Dislocation Mechanics framework offers the intriguing possibility of serving as a general mathematical setting for modeling the meso and macroscale behavior in diverse applications like earthquake rupture dynamics and amorphous materials like metallic glasses, when characterized by appropriate physics related to material response. Such a development is being actively pursued as a collaboration between Professors Maloney, Bielak, and Acharya along with Professors Luc Tartar and Noel Walkington in the CMU Mathematics department and collaborators in Engineering and Materials Science at the University of Illinois at Urbana- Champaign, and the Paul Scherrer Institute in Switzerland.
Shear Localization in Metallic Glasses
Metallic glasses are an emerging class of engineering materials which offer the high formability of thermo-plastics along with the high strength of metallic alloys. These are desirable properties for applications ranging from civil infrastructure to defense. Unfortunately, as their failure modes are not yet well understood, critical applications are currently out of the question. One common failure mode for metallic glasses involves bands of intense shear strain that develop when samples are pulled in tension. The origin of these bands is currently a matter of debate.
Professor Maloney performs computer simulations of these metallic glasses at the level of individual atoms. Figure 3 shows a simulation containing a 2 dimensional slice of 1.6 million atoms. Simulations like these take several days of dedicated time on a cluster of more than 100 CPUs. The sample is being compressed vertically, and the color represents horizontal displacement in a short window of time. Shear strain appears as a sharp gradient in color. The width of the bands that emerge in the simulations is only a few atomic spacings, while the ones observed in the laboratory are thousands of times wider. However, the atomic scale bands seen in the computer simulations form in a correlated way, with new bands forming preferentially near existing ones. Prof. Maloney is currently working with Prof. Acharya to develop meso-scale descriptions, within the Field Dislocation Mechanics framework, using the atomic scale simulations to parameterize the meso-scale models.
Understanding Active Materials
Active materials display unusual couplings between deformation, temperature, optics, and electromagnetism. Current research and development of micro-nano electromechanical systems (MEMS/NEMS) provides new opportunities for exploiting these unusual materials. These opportunities also require a fundamental understanding of the behavior of active materials at these small scales, especially in dynamic settings.
Professor Dayal's research aims at formulating mesoscopic models and developing numerical techniques to aid design and fabrication of active nanoscale devices. Currently, he focuses on using ferroelectrics to design new optical switching devices and microwave circuit elements. A parallel study aims at an atomic-level understanding of instability, nucleation, and kinetics of microstructural elements in active materials. This will enable development of atomistically-informed mesoscopic models, and provide multiscale capabilities to understand and exploit these complex materials.
In the figure 4, a ferroelectric specimen is subjected to mechanical loads. This leads to complex deformations near the tip of notch. The electric fields can lead to the motion of electrical impurities (or 'dopants') and is a potential failure mechanism that is currently being researched.
End-to-end Earthquake Modeling/Infrastructure Response
To prevent earthquakes from becoming disasters, it is essential to gain a better understanding of how earthquakes originate, how the seismic waves propagate from the source, how they amplify as they enter alluvial basins, and how the built environment responds to such excitation. Professor Bielak is working on different aspects of this problem, including the forward and inverse-based simulation of the earthquake ground motion in large basins (figure 5) using high performance computing, and on the effect of this ground motion on portions of an entire city, including buildings, bridges, and underground structures. In addition, he and Professor Acharya use concepts of dislocation mechanics to study the dynamic rupture process on faults. The objective is to be able to generate realistic scenario earthquakes that can be used as input in end-to-end, or "rupture to rivets", simulations.
Coarse-Graining Nonlinear Dynamics of Materials Systems
The question of deducing the general form and specifics of the laws governing macroscopic response of materials based on well-established microscopic theories is essentially a mathematical and algorithmic one. Professor Acharya's approach to this problem starts from a given fine dynamics with some idea of what time-averaged coarse variables (i.e. time averages of aggregated degrees of freedom) one might be interested in. This microscopic dynamics is augmented by the addition of appropriate forward and backward time-delay variables corresponding to the original set so that an appropriate macroscopic dynamics becomes associated with it that may be computationally approximated. In essence, a practically crucial time-scale separation is induced by the augmentation even if the original dynamics did not come equipped with one. The development and implementation of this methodology involves sophisticated tools from nonlinear mathematics, statistical inference, numerical analysis, database management and data-mining. This work has been successfully applied to small, but difficult, nonlinear problems as proof-of-principle, as recorded in the technical literature.
Professors Acharya, Dayal, and Maloney, in collaboration with Prof. Lucio Soibelman (AIS), Profs. Tartar and Walkington (Mathematics), Prof. Erik Ydstie (Chemical Engineering) along with colleagues at the Pittsburgh Supercomputing Center, the National Energy Technology Labs and applied mathematicians at the Univ. of Leicester, UK, and Rennes 1, CNRS (National Center for Scientific Research), France, are in the process of applying these ideas to a variety of practical problems in solid mechanics, biology, chemical engineering, and fluid dynamics.